Mod-2-Cohomology of MathieuGroup(21), a group of order 20160

About the group Ring generators Ring relations Completion information Restriction maps

General information on the group

  • MathieuGroup(21) is a group of order 20160.
  • The group order factors as 26 · 32 · 5 · 7.
  • The group is defined by Group([(1,4,5,9,3)(2,8,10,7,6)(12,15,16,20,14)(13,19,21,18,17),(1,21,5,12,20)(2,16,3,4,17)(6,18,7,19,15)(8,13,9,14,11)]).
  • It is non-abelian.
  • It has 2-Rank 4.
  • The centre of a Sylow 2-subgroup has rank 2.
  • Its Sylow 2-subgroup has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 4.

Structure of the cohomology ring

The computation was based on 4 stability conditions for H*(SmallGroup(192,1023); GF(2)).

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    1  −  t  +  3·t2  −  2·t3  +  t4  +  t5  +  t6  −  2·t7  +  5·t8  −  t9  +  3·t11  −  t12  +  3·t14  +  t15  −  3·t16  +  4·t17  −  3·t18  +  t19  +  t20
    (1  +  t) · ( − 1  +  t)4 · (1  −  t  +  t2) · (1  +  t2)2 · (1  +  t  +  t2)2 · (1  −  t2  +  t4) · (1  +  t  +  t2  +  t3  +  t4)
  • The a-invariants are -∞,-∞,-3,-5,-4. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].

About the group Ring generators Ring relations Completion information Restriction maps

Ring generators

The cohomology ring has 18 minimal generators of maximal degree 12:

  1. a_2_1, a nilpotent element of degree 2
  2. a_2_0, a nilpotent element of degree 2
  3. b_3_1, an element of degree 3
  4. b_3_0, an element of degree 3
  5. b_5_3, an element of degree 5
  6. b_5_2, an element of degree 5
  7. b_5_1, an element of degree 5
  8. b_5_0, an element of degree 5
  9. b_6_5, an element of degree 6
  10. b_6_3, an element of degree 6
  11. b_6_0, an element of degree 6
  12. c_8_8, a Duflot element of degree 8
  13. b_9_3, an element of degree 9
  14. b_9_2, an element of degree 9
  15. b_9_1, an element of degree 9
  16. b_9_0, an element of degree 9
  17. c_12_1, a Duflot element of degree 12
  18. c_12_0, a Duflot element of degree 12

About the group Ring generators Ring relations Completion information Restriction maps

Ring relations

There are 99 minimal relations of maximal degree 24:

  1. a_2_02
  2. a_2_0·a_2_1
  3. a_2_12
  4. a_2_0·b_3_1
  5. a_2_1·b_3_0
  6. a_2_1·b_3_1 + a_2_0·b_3_0
  7. a_2_0·b_5_2 + a_2_0·b_5_0
  8. a_2_0·b_5_3 + a_2_0·b_5_1
  9. a_2_1·b_5_0 + a_2_0·b_5_1
  10. a_2_1·b_5_1 + a_2_0·b_5_1 + a_2_0·b_5_0
  11. a_2_1·b_5_2 + a_2_0·b_5_1 + a_2_0·b_5_0
  12. a_2_1·b_5_3 + a_2_0·b_5_0
  13. a_2_0·b_6_0
  14. a_2_0·b_6_3
  15. a_2_0·b_6_5
  16. a_2_1·b_6_0
  17. a_2_1·b_6_3
  18. a_2_1·b_6_5
  19. b_3_0·b_3_12 + b_3_02·b_3_1 + b_6_3·b_3_1 + b_6_3·b_3_0 + b_6_0·b_3_0
  20. b_3_13 + b_3_02·b_3_1 + b_6_5·b_3_0 + b_6_0·b_3_1 + b_6_0·b_3_0
  21. b_5_0·b_5_2 + a_2_0·c_8_8
  22. b_5_0·b_5_3 + a_2_1·c_8_8 + a_2_0·c_8_8
  23. b_5_1·b_5_2 + a_2_1·c_8_8
  24. b_5_1·b_5_3 + a_2_0·c_8_8
  25. a_2_0·b_9_2 + a_2_0·b_9_1
  26. a_2_0·b_9_3 + a_2_0·b_9_1 + a_2_0·b_9_0
  27. a_2_1·b_9_0 + a_2_0·b_9_1
  28. a_2_1·b_9_1 + a_2_0·b_9_1 + a_2_0·b_9_0
  29. a_2_1·b_9_2 + a_2_0·b_9_0
  30. a_2_1·b_9_3 + a_2_0·b_9_1
  31. b_6_3·b_5_2 + a_2_0·b_9_1
  32. b_6_3·b_5_3 + a_2_0·b_9_0
  33. b_6_5·b_5_0 + b_6_0·b_5_0 + a_2_0·b_9_1 + a_2_0·b_9_0
  34. b_6_5·b_5_1 + b_6_0·b_5_1 + a_2_0·b_9_1
  35. b_6_5·b_5_2 + a_2_0·b_9_1 + a_2_0·b_9_0
  36. b_6_5·b_5_3 + a_2_0·b_9_1
  37. b_3_02·b_5_0 + b_6_3·b_5_0 + a_2_0·b_9_1 + a_2_0·b_9_0
  38. b_3_02·b_5_1 + b_6_3·b_5_1 + a_2_0·b_9_1
  39. b_3_12·b_5_0 + b_6_3·b_5_0 + b_6_0·b_5_0 + a_2_0·b_9_1
  40. b_3_12·b_5_1 + b_6_3·b_5_1 + b_6_0·b_5_1 + a_2_0·b_9_0
  41. b_3_12·b_5_2 + b_3_0·b_3_1·b_5_2 + b_6_0·b_5_2 + a_2_0·b_9_0
  42. b_3_12·b_5_3 + b_3_0·b_3_1·b_5_3 + b_6_0·b_5_3 + a_2_0·b_9_1 + a_2_0·b_9_0
  43. b_6_3·b_6_5 + b_6_0·b_6_3
  44. b_6_3·b_3_02 + b_6_32
  45. b_6_3·b_3_12 + b_6_32 + b_6_0·b_6_3
  46. b_6_52 + b_6_0·b_6_5
  47. b_6_5·b_3_0·b_3_1 + b_6_0·b_3_12 + b_6_0·b_3_0·b_3_1 + b_6_0·b_6_3 + b_6_02
  48. b_6_5·b_3_12 + b_6_0·b_6_5 + b_6_0·b_6_3
  49. b_5_0·b_9_2 + b_6_3·b_3_1·b_5_0 + b_6_0·b_3_0·b_5_0 + a_2_1·c_12_1 + a_2_1·c_12_0
       + a_2_0·c_12_1
  50. b_5_0·b_9_3 + b_6_3·b_3_1·b_5_0 + b_6_3·b_3_0·b_5_0 + a_2_1·c_12_1 + a_2_0·c_12_0
  51. b_5_1·b_9_0 + b_5_0·b_9_1 + b_5_0·b_9_0 + b_6_3·b_3_1·b_5_1 + b_6_3·b_3_1·b_5_0
       + b_6_3·b_3_0·b_5_1 + b_6_3·b_3_0·b_5_0 + b_6_0·b_3_1·b_5_0 + b_6_0·b_3_0·b_5_1
       + b_6_0·b_3_0·b_5_0 + b_6_5·c_8_8 + b_6_3·c_8_8
  52. b_5_1·b_9_1 + b_5_0·b_9_0 + b_6_3·b_3_1·b_5_0 + b_6_3·b_3_0·b_5_1 + b_6_3·b_3_0·b_5_0
       + b_6_0·b_3_1·b_5_0 + b_6_0·b_3_0·b_5_1 + b_6_3·c_8_8
  53. b_5_1·b_9_2 + b_6_3·b_3_1·b_5_1 + b_6_0·b_3_0·b_5_1 + a_2_1·c_12_0 + a_2_0·c_12_1
       + a_2_0·c_12_0
  54. b_5_1·b_9_3 + b_6_3·b_3_1·b_5_1 + b_6_3·b_3_0·b_5_1 + a_2_1·c_12_1 + a_2_1·c_12_0
       + a_2_0·c_12_1
  55. b_5_2·b_9_0 + a_2_1·c_12_0 + a_2_0·c_12_1
  56. b_5_2·b_9_1 + a_2_1·c_12_1 + a_2_1·c_12_0 + a_2_0·c_12_0
  57. b_5_3·b_9_0 + a_2_1·c_12_1 + a_2_0·c_12_1 + a_2_0·c_12_0
  58. b_5_3·b_9_1 + a_2_1·c_12_0 + a_2_0·c_12_1
  59. b_5_3·b_9_2 + b_5_2·b_9_3 + b_5_2·b_9_2 + b_3_02·b_3_1·b_5_3 + b_3_02·b_3_1·b_5_2
       + b_3_03·b_5_3 + b_3_03·b_5_2 + b_6_0·b_3_1·b_5_2 + b_6_0·b_3_0·b_5_2 + c_8_8·b_3_12
       + c_8_8·b_3_02 + b_6_5·c_8_8
  60. b_5_3·b_9_3 + b_5_2·b_9_2 + b_3_02·b_3_1·b_5_3 + b_3_02·b_3_1·b_5_2 + b_3_03·b_5_3
       + b_6_0·b_3_1·b_5_3 + b_6_0·b_3_0·b_5_3 + b_6_0·b_3_0·b_5_2 + c_8_8·b_3_02
       + b_6_3·c_8_8
  61. b_6_3·b_9_2 + b_6_32·b_3_1 + b_6_0·b_6_3·b_3_0 + a_2_0·c_8_8·b_5_0
  62. b_6_3·b_9_3 + b_6_32·b_3_1 + b_6_32·b_3_0 + a_2_0·c_8_8·b_5_1 + a_2_0·c_8_8·b_5_0
  63. b_6_5·b_9_0 + b_6_0·b_9_0 + a_2_0·c_8_8·b_5_1 + a_2_0·c_8_8·b_5_0
  64. b_6_5·b_9_1 + b_6_0·b_9_1 + a_2_0·c_8_8·b_5_1
  65. b_6_5·b_9_2 + b_6_0·b_6_5·b_3_0 + b_6_0·b_6_3·b_3_1 + a_2_0·c_8_8·b_5_1
  66. b_6_5·b_9_3 + b_6_0·b_6_3·b_3_1 + b_6_0·b_6_3·b_3_0 + a_2_0·c_8_8·b_5_0
  67. b_3_02·b_9_0 + b_6_3·b_9_0 + a_2_0·c_8_8·b_5_1 + a_2_0·c_8_8·b_5_0
  68. b_3_02·b_9_1 + b_6_3·b_9_1 + a_2_0·c_8_8·b_5_1
  69. b_3_12·b_9_0 + b_6_3·b_9_0 + b_6_0·b_9_0 + a_2_0·c_8_8·b_5_1
  70. b_3_12·b_9_1 + b_6_3·b_9_1 + b_6_0·b_9_1 + a_2_0·c_8_8·b_5_0
  71. b_3_12·b_9_2 + b_3_0·b_3_1·b_9_2 + b_6_32·b_3_1 + b_6_32·b_3_0 + b_6_0·b_9_2
       + b_6_0·b_6_3·b_3_1 + a_2_0·c_8_8·b_5_1 + a_2_0·c_8_8·b_5_0
  72. b_3_12·b_9_3 + b_3_0·b_3_1·b_9_3 + b_6_0·b_9_3 + b_6_0·b_6_3·b_3_0 + a_2_0·c_8_8·b_5_1
  73. b_5_0·b_5_12 + b_5_02·b_5_1 + b_5_03 + b_6_3·b_9_1 + b_6_3·b_9_0 + b_6_32·b_3_1
       + b_6_0·b_9_1 + b_6_0·b_6_5·b_3_0 + b_6_0·b_6_3·b_3_0 + a_2_0·c_8_8·b_5_1
  74. b_5_13 + b_5_03 + b_6_3·b_9_0 + b_6_32·b_3_1 + b_6_0·b_9_1 + b_6_0·b_9_0
       + b_6_0·b_6_5·b_3_1 + b_6_0·b_6_5·b_3_0 + b_6_0·b_6_3·b_3_1 + b_6_0·b_6_3·b_3_0
       + a_2_0·c_8_8·b_5_0
  75. b_5_2·b_5_32 + b_5_22·b_5_3 + b_5_23 + b_3_0·b_3_1·b_9_3 + b_3_02·b_9_3
       + b_3_02·b_9_2 + b_6_32·b_3_1 + b_6_0·b_9_3 + b_6_0·b_3_03 + b_6_0·b_6_5·b_3_1
       + b_6_0·b_6_3·b_3_1 + b_6_02·b_3_1 + a_2_0·c_8_8·b_5_1
  76. b_5_33 + b_5_23 + b_3_0·b_3_1·b_9_3 + b_3_0·b_3_1·b_9_2 + b_3_02·b_9_2
       + b_3_04·b_3_1 + b_3_05 + b_6_32·b_3_1 + b_6_32·b_3_0 + b_6_0·b_9_3 + b_6_0·b_9_2
       + b_6_0·b_3_02·b_3_1 + b_6_0·b_6_5·b_3_1 + b_6_02·b_3_1 + b_6_02·b_3_0
       + a_2_0·c_8_8·b_5_0
  77. b_3_1·b_5_0·b_9_0 + b_6_3·b_3_0·b_3_1·b_5_1 + b_6_32·b_5_0 + b_6_0·b_3_0·b_3_1·b_5_0
       + b_6_0·b_6_3·b_5_1 + b_6_02·b_5_1 + c_12_1·b_5_0 + c_12_0·b_5_1 + c_8_8·b_9_0
       + b_6_5·c_8_8·b_3_1 + b_6_3·c_8_8·b_3_1
  78. b_3_1·b_5_0·b_9_1 + b_6_3·b_3_0·b_3_1·b_5_1 + b_6_3·b_3_0·b_3_1·b_5_0 + b_6_32·b_5_1
       + b_6_32·b_5_0 + b_6_0·b_3_0·b_3_1·b_5_1 + b_6_0·b_3_0·b_3_1·b_5_0 + b_6_0·b_6_3·b_5_1
       + b_6_0·b_6_3·b_5_0 + b_6_02·b_5_1 + b_6_02·b_5_0 + c_12_1·b_5_1 + c_12_0·b_5_1
       + c_12_0·b_5_0 + c_8_8·b_9_1 + b_6_5·c_8_8·b_3_1 + b_6_3·c_8_8·b_3_0
  79. b_3_1·b_5_2·b_9_2 + b_3_04·b_5_3 + b_6_0·b_3_0·b_3_1·b_5_2 + b_6_02·b_5_2
       + c_12_1·b_5_3 + c_12_1·b_5_2 + c_12_0·b_5_2 + c_8_8·b_9_3 + c_8_8·b_3_03
       + b_6_5·c_8_8·b_3_0 + b_6_3·c_8_8·b_3_1 + b_6_0·c_8_8·b_3_0
  80. b_3_1·b_5_2·b_9_3 + b_3_03·b_3_1·b_5_3 + b_3_04·b_5_3 + b_3_04·b_5_2
       + b_6_0·b_3_0·b_3_1·b_5_3 + b_6_0·b_3_02·b_5_3 + b_6_02·b_5_3 + b_6_02·b_5_2
       + c_12_1·b_5_2 + c_12_0·b_5_3 + c_8_8·b_9_3 + c_8_8·b_9_2 + b_6_5·c_8_8·b_3_0
       + b_6_3·c_8_8·b_3_0
  81. b_3_1·b_5_03 + b_6_3·b_3_0·b_9_1 + b_6_0·b_3_1·b_9_1 + b_6_0·b_3_1·b_9_0
       + b_6_0·b_3_0·b_9_1 + b_6_0·b_3_0·b_9_0 + b_6_0·b_6_3·b_3_0·b_3_1 + b_6_0·b_6_32
       + b_6_02·b_3_12 + b_6_02·b_3_0·b_3_1 + b_6_02·b_6_5 + b_6_02·b_6_3 + b_6_03
       + c_8_8·b_5_02 + b_6_5·c_12_1 + b_6_5·c_12_0 + b_6_3·c_12_1
  82. b_3_1·b_5_02·b_5_1 + b_6_3·b_3_1·b_9_1 + b_6_3·b_3_1·b_9_0 + b_6_3·b_3_0·b_9_0
       + b_6_33 + b_6_0·b_3_0·b_9_1 + b_6_02·b_6_5 + b_6_02·b_6_3 + c_8_8·b_5_12
       + c_8_8·b_5_02 + b_6_5·c_12_0 + b_6_3·c_12_1 + b_6_3·c_12_0
  83. b_3_1·b_5_23 + b_3_02·b_3_1·b_9_3 + b_3_02·b_3_1·b_9_2 + b_3_05·b_3_1
       + b_6_0·b_3_1·b_9_2 + b_6_0·b_3_04 + b_6_0·b_6_3·b_3_0·b_3_1 + b_6_02·b_3_12
       + b_6_02·b_3_0·b_3_1 + b_6_02·b_3_02 + b_6_02·b_6_5 + b_6_02·b_6_3
       + c_12_1·b_3_02 + c_12_0·b_3_12 + c_12_0·b_3_02 + c_8_8·b_5_32 + b_6_5·c_12_0
       + b_6_3·c_12_1
  84. b_3_1·b_5_22·b_5_3 + b_3_02·b_3_1·b_9_3 + b_3_02·b_3_1·b_9_2 + b_3_06
       + b_6_32·b_3_0·b_3_1 + b_6_33 + b_6_0·b_3_1·b_9_2 + b_6_0·b_3_0·b_9_3 + b_6_0·b_3_04
       + b_6_0·b_6_32 + b_6_02·b_3_0·b_3_1 + b_6_02·b_6_3 + c_12_1·b_3_12
       + c_12_0·b_3_02 + c_8_8·b_5_22 + b_6_5·c_12_1 + b_6_3·c_12_1 + b_6_3·c_12_0
  85. b_9_02 + b_3_0·b_5_03 + b_6_3·b_3_0·b_9_1 + b_6_33 + b_6_0·b_6_3·b_3_0·b_3_1
       + b_6_0·b_6_32 + b_6_02·b_3_12 + b_6_02·b_3_0·b_3_1 + b_6_02·b_6_5 + b_6_02·b_6_3
       + b_6_03 + c_8_8·b_5_12 + c_8_8·b_5_02 + b_6_5·c_12_1 + b_6_5·c_12_0
  86. b_9_0·b_9_1 + b_3_0·b_5_02·b_5_1 + b_3_0·b_5_03 + b_6_3·b_3_1·b_9_1
       + b_6_3·b_3_0·b_9_0 + b_6_32·b_3_0·b_3_1 + b_6_0·b_3_1·b_9_1 + b_6_0·b_3_1·b_9_0
       + b_6_0·b_3_0·b_9_1 + b_6_02·b_3_12 + b_6_02·b_3_0·b_3_1 + b_6_03 + c_8_8·b_5_12
       + c_8_8·b_5_0·b_5_1 + b_6_5·c_12_1
  87. b_9_0·b_9_2 + b_6_3·b_3_1·b_9_0 + b_6_0·b_3_0·b_9_0 + a_2_1·c_8_82 + a_2_0·c_8_82
  88. b_9_0·b_9_3 + b_6_3·b_3_1·b_9_0 + b_6_3·b_3_0·b_9_0 + a_2_1·c_8_82
  89. b_9_12 + b_3_0·b_5_02·b_5_1 + b_6_3·b_3_0·b_9_1 + b_6_0·b_3_0·b_9_1
       + b_6_0·b_6_3·b_3_0·b_3_1 + b_6_02·b_6_5 + b_6_02·b_6_3 + c_8_8·b_5_12 + b_6_5·c_12_0
  90. b_9_1·b_9_2 + b_6_3·b_3_1·b_9_1 + b_6_0·b_3_0·b_9_1 + a_2_0·c_8_82
  91. b_9_1·b_9_3 + b_6_3·b_3_1·b_9_1 + b_6_3·b_3_0·b_9_1 + a_2_1·c_8_82 + a_2_0·c_8_82
  92. b_9_22 + b_3_0·b_5_22·b_5_3 + b_3_02·b_3_1·b_9_3 + b_3_02·b_3_1·b_9_2
       + b_3_03·b_9_3 + b_3_03·b_9_2 + b_6_32·b_3_0·b_3_1 + b_6_0·b_3_0·b_9_2
       + b_6_0·b_3_03·b_3_1 + b_6_0·b_6_3·b_3_0·b_3_1 + c_12_0·b_3_02 + c_8_8·b_5_32
       + b_6_3·c_12_0
  93. b_9_2·b_9_3 + b_3_0·b_5_23 + b_3_02·b_3_1·b_9_3 + b_3_02·b_3_1·b_9_2 + b_3_06
       + b_6_0·b_3_1·b_9_2 + b_6_0·b_3_0·b_9_2 + b_6_0·b_3_03·b_3_1 + b_6_0·b_6_32
       + b_6_02·b_3_12 + b_6_02·b_3_0·b_3_1 + b_6_02·b_6_3 + b_6_03 + c_12_1·b_3_02
       + c_12_0·b_3_02 + c_8_8·b_5_2·b_5_3 + b_6_3·c_12_1 + b_6_3·c_12_0
  94. b_9_32 + b_3_0·b_5_22·b_5_3 + b_3_0·b_5_23 + b_3_02·b_3_1·b_9_2 + b_3_03·b_9_3
       + b_3_03·b_9_2 + b_3_05·b_3_1 + b_6_32·b_3_0·b_3_1 + b_6_0·b_3_03·b_3_1
       + b_6_0·b_3_04 + b_6_02·b_3_12 + b_6_02·b_3_02 + b_6_02·b_6_5 + c_12_1·b_3_02
       + c_8_8·b_5_22 + b_6_3·c_12_1
  95. b_6_32·b_9_1 + b_6_33·b_3_1 + b_6_0·b_3_0·b_3_1·b_9_1 + b_6_0·b_3_0·b_3_1·b_9_0
       + b_6_0·b_6_3·b_9_0 + b_6_0·b_6_32·b_3_1 + b_6_0·b_6_32·b_3_0 + b_6_02·b_9_1
       + b_6_02·b_9_0 + b_6_02·b_6_5·b_3_0 + c_12_1·b_9_0 + c_12_0·b_9_1 + c_12_0·b_9_0
       + c_8_8·b_3_1·b_5_02 + b_6_5·c_12_1·b_3_1 + b_6_3·c_12_1·b_3_1 + b_6_3·c_12_0·b_3_1
       + b_6_3·c_12_0·b_3_0 + c_8_82·b_5_0
  96. b_6_3·b_3_0·b_3_1·b_9_1 + b_6_32·b_9_0 + b_6_0·b_3_0·b_3_1·b_9_0
       + b_6_0·b_6_32·b_3_0 + b_6_02·b_9_0 + b_6_02·b_6_5·b_3_1 + b_6_02·b_6_3·b_3_1
       + c_12_1·b_9_1 + c_12_1·b_9_0 + c_12_0·b_9_1 + c_8_8·b_3_1·b_5_0·b_5_1
       + c_8_8·b_3_1·b_5_02 + b_6_5·c_12_0·b_3_1 + b_6_3·c_12_1·b_3_1 + b_6_3·c_12_1·b_3_0
       + b_6_3·c_12_0·b_3_0 + c_8_82·b_5_1 + c_8_82·b_5_0 + a_2_0·c_8_82·b_3_0
  97. b_3_04·b_9_2 + b_3_07 + b_6_33·b_3_1 + b_6_33·b_3_0 + b_6_0·b_5_22·b_5_3
       + b_6_0·b_3_0·b_3_1·b_9_2 + b_6_0·b_3_02·b_9_3 + b_6_0·b_3_02·b_9_2 + b_6_0·b_3_05
       + b_6_02·b_9_3 + b_6_02·b_9_2 + b_6_02·b_3_02·b_3_1 + b_6_02·b_6_5·b_3_1
       + b_6_02·b_6_5·b_3_0 + b_6_02·b_6_3·b_3_0 + b_6_03·b_3_1 + c_12_1·b_9_3 + c_12_1·b_9_2
       + c_12_1·b_3_02·b_3_1 + c_12_0·b_9_3 + c_12_0·b_3_03 + c_8_8·b_3_1·b_5_32
       + c_8_8·b_3_0·b_5_22 + b_6_5·c_12_1·b_3_0 + b_6_5·c_12_0·b_3_1 + b_6_3·c_12_1·b_3_1
       + b_6_3·c_12_1·b_3_0 + b_6_3·c_12_0·b_3_1 + b_6_0·c_12_0·b_3_1 + c_8_82·b_5_2
  98. b_3_03·b_3_1·b_9_3 + b_3_03·b_3_1·b_9_2 + b_3_04·b_9_3 + b_6_33·b_3_0
       + b_6_0·b_3_0·b_3_1·b_9_3 + b_6_0·b_3_02·b_9_3 + b_6_0·b_3_04·b_3_1 + b_6_02·b_9_3
       + b_6_02·b_9_2 + b_6_02·b_3_02·b_3_1 + b_6_02·b_3_03 + b_6_02·b_6_5·b_3_1
       + b_6_02·b_6_3·b_3_1 + b_6_02·b_6_3·b_3_0 + b_6_03·b_3_1 + b_6_03·b_3_0
       + c_12_1·b_9_2 + c_12_0·b_9_3 + c_12_0·b_9_2 + c_12_0·b_3_02·b_3_1
       + c_8_8·b_3_1·b_5_2·b_5_3 + c_8_8·b_3_1·b_5_22 + c_8_8·b_3_0·b_5_32
       + c_8_8·b_3_0·b_5_2·b_5_3 + c_8_8·b_3_0·b_5_22 + b_6_5·c_12_1·b_3_0
       + b_6_5·c_12_0·b_3_1 + b_6_5·c_12_0·b_3_0 + b_6_3·c_12_1·b_3_1 + b_6_3·c_12_0·b_3_1
       + b_6_3·c_12_0·b_3_0 + b_6_0·c_12_0·b_3_1 + c_8_82·b_5_3
  99. b_3_05·b_9_3 + b_6_33·b_3_0·b_3_1 + b_6_0·b_3_0·b_5_22·b_5_3
       + b_6_0·b_3_02·b_3_1·b_9_2 + b_6_0·b_3_03·b_9_3 + b_6_0·b_3_05·b_3_1
       + b_6_0·b_6_3·b_3_1·b_9_1 + b_6_0·b_6_3·b_3_1·b_9_0 + b_6_0·b_6_3·b_3_0·b_9_1
       + b_6_02·b_3_1·b_9_3 + b_6_02·b_3_1·b_9_2 + b_6_02·b_3_1·b_9_0 + b_6_02·b_3_0·b_9_1
       + b_6_02·b_3_03·b_3_1 + b_6_02·b_3_04 + b_6_03·b_3_0·b_3_1 + b_6_03·b_3_02
       + c_12_1·b_3_1·b_9_2 + c_12_1·b_3_1·b_9_1 + c_12_1·b_3_1·b_9_0 + c_12_1·b_3_0·b_9_2
       + c_12_1·b_3_0·b_9_1 + c_12_1·b_3_0·b_9_0 + c_12_1·b_3_04 + c_12_0·b_3_1·b_9_3
       + c_12_0·b_3_1·b_9_2 + c_12_0·b_3_1·b_9_1 + c_12_0·b_3_0·b_9_3 + c_12_0·b_3_0·b_9_2
       + c_12_0·b_3_0·b_9_1 + c_8_8·b_3_0·b_3_1·b_5_22 + c_8_8·b_3_0·b_3_1·b_5_12
       + c_8_8·b_3_02·b_5_32 + c_8_8·b_3_02·b_5_2·b_5_3 + b_6_3·c_12_0·b_3_0·b_3_1
       + b_6_3·c_8_8·b_5_12 + b_6_3·c_8_8·b_5_02 + b_6_32·c_12_1 + b_6_32·c_12_0
       + b_6_0·c_12_1·b_3_0·b_3_1 + b_6_0·c_8_8·b_5_32 + b_6_0·c_8_8·b_5_2·b_5_3
       + b_6_0·c_8_8·b_5_0·b_5_1 + b_6_0·b_6_5·c_12_1 + b_6_0·b_6_3·c_12_0 + b_6_02·c_12_1
       + b_6_02·c_12_0 + c_12_12 + c_12_0·c_12_1 + c_12_02 + c_8_82·b_3_1·b_5_2
       + c_8_82·b_3_1·b_5_1 + c_8_82·b_3_1·b_5_0 + c_8_82·b_3_0·b_5_3 + c_8_82·b_3_0·b_5_2
       + c_8_82·b_3_0·b_5_1 + c_8_82·b_3_0·b_5_0 + c_8_83

About the group Ring generators Ring relations Completion information Restriction maps

Data used for the Hilbert-Poincaré test

  • We proved completion in degree 26 using the Hilbert-Poincaré criterion.
  • However, the last relation was already found in degree 24 and the last generator in degree 12.
  • The following is a filter regular homogeneous system of parameters:
    1. b_3_1·b_5_1 + b_3_0·b_5_2 + b_3_0·b_5_0 + c_8_8, an element of degree 8
    2. b_3_1·b_9_3 + b_3_1·b_9_1 + b_3_0·b_9_0 + b_3_03·b_3_1 + b_6_0·b_6_5 + b_6_0·b_6_3
         + b_6_02 + c_12_0, an element of degree 12
    3. b_5_2·b_9_3 + b_5_2·b_9_2 + b_5_0·b_9_0 + b_3_02·b_3_1·b_5_2 + b_6_3·b_3_1·b_5_1
         + b_6_3·b_3_1·b_5_0 + b_6_3·b_3_0·b_5_0 + b_6_0·b_3_1·b_5_2 + b_6_0·b_3_1·b_5_1
         + b_6_0·b_3_1·b_5_0 + b_6_0·b_3_0·b_5_2 + b_6_0·b_3_0·b_5_0 + c_8_8·b_3_12, an element of degree 14
    4. b_5_23 + b_5_03 + b_3_0·b_3_1·b_9_3 + b_3_0·b_3_1·b_9_2 + b_6_3·b_9_0 + b_6_0·b_9_3
         + b_6_0·b_9_2 + b_6_0·b_9_0 + b_6_0·b_3_02·b_3_1 + b_6_0·b_6_3·b_3_0 + b_6_02·b_3_1
         + b_6_02·b_3_0, an element of degree 15
  • A Duflot regular sequence is given by c_8_8, c_12_1.
  • The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, 17, 29, 45].
  • Modifying the above filter regular HSOP, we obtained the following parameters:
    1. b_3_1·b_5_1 + b_3_0·b_5_2 + b_3_0·b_5_0 + c_8_8, an element of degree 8
    2. b_3_1·b_9_3 + b_3_1·b_9_1 + b_3_0·b_9_0 + b_3_03·b_3_1 + b_6_0·b_6_5 + b_6_0·b_6_3
         + b_6_02 + c_12_0, an element of degree 12
    3. b_3_0, an element of degree 3
    4. b_5_2 + b_5_0, an element of degree 5

About the group Ring generators Ring relations Completion information Restriction maps

Restriction maps

Expressing the generators as elements of H*(SmallGroup(192,1023); GF(2))

  1. a_2_1 → a_2_2
  2. a_2_0 → a_2_3
  3. b_3_1 → b_3_1
  4. b_3_0 → b_3_5 + b_3_0
  5. b_5_3 → b_5_8 + b_2_1·b_3_0
  6. b_5_2 → b_5_9
  7. b_5_1 → b_5_11 + b_2_1·b_3_1 + b_2_0·b_3_1
  8. b_5_0 → b_5_12
  9. b_6_5 → b_3_0·b_3_5 + b_3_0·b_3_4 + b_3_0·b_3_2 + b_6_18
  10. b_6_3 → b_3_1·b_3_4 + b_3_1·b_3_3 + b_3_1·b_3_2 + b_3_0·b_3_4 + b_3_0·b_3_3 + b_3_0·b_3_2 + b_6_19
       + b_6_18
  11. b_6_0 → b_3_2·b_3_5 + b_3_1·b_3_3 + b_3_0·b_3_3 + b_3_0·b_3_1 + b_3_02 + b_6_19 + b_6_18 + b_6_7
  12. c_8_8 → b_2_0·b_3_2·b_3_5 + b_2_0·b_3_1·b_3_4 + b_2_0·b_3_1·b_3_3 + b_2_0·b_3_12
       + b_2_0·b_3_0·b_3_3 + b_2_0·b_3_02 + b_2_0·b_6_19 + b_2_0·b_6_18 + b_2_0·b_6_7 + b_2_04
       + c_8_32
  13. b_9_3 → b_9_26 + b_3_02·b_3_3 + b_6_18·b_3_3 + b_6_18·b_3_2 + b_6_18·b_3_1 + b_6_7·b_3_5
       + b_6_7·b_3_2 + b_6_7·b_3_1 + b_6_7·b_3_0 + b_2_02·b_5_11 + b_2_03·b_3_1 + b_2_03·b_3_0
  14. b_9_2 → b_9_33 + b_3_0·b_3_1·b_3_2 + b_3_0·b_3_12 + b_3_02·b_3_3 + b_3_02·b_3_1 + b_6_18·b_3_3
       + b_6_18·b_3_2 + b_6_18·b_3_1 + b_6_18·b_3_0 + b_6_7·b_3_4 + b_6_7·b_3_2 + b_6_7·b_3_1
       + b_2_02·b_5_11 + b_2_02·b_5_9 + b_2_02·b_2_1·b_3_1 + b_2_03·b_3_1 + b_2_03·b_3_0
  15. b_9_1 → b_9_42 + b_6_19·b_3_1 + b_6_19·b_3_0 + b_6_18·b_3_2 + b_6_18·b_3_0 + b_6_7·b_3_5
       + b_6_7·b_3_4 + b_6_7·b_3_2 + b_2_02·b_5_12 + b_2_02·b_5_11 + b_2_02·b_2_1·b_3_1
       + b_2_03·b_3_1
  16. b_9_0 → b_9_43 + b_6_18·b_3_2 + b_2_02·b_5_11 + b_2_02·b_2_1·b_3_1 + b_2_03·b_3_1
  17. c_12_1 → b_3_24 + b_3_03·b_3_3 + b_3_03·b_3_2 + b_3_03·b_3_1 + b_3_04 + b_6_18·b_3_02
       + b_6_18·b_6_19 + b_6_7·b_3_2·b_3_5 + b_6_7·b_3_2·b_3_4 + b_6_7·b_3_1·b_3_5
       + b_6_7·b_3_1·b_3_2 + b_6_7·b_3_12 + b_6_7·b_3_0·b_3_2 + b_6_7·b_3_0·b_3_1
       + b_6_7·b_3_02 + b_2_0·b_5_8·b_5_9 + b_2_02·b_3_0·b_5_12 + b_2_02·b_3_0·b_5_9
       + b_2_03·b_3_2·b_3_4 + b_2_03·b_3_1·b_3_4 + b_2_03·b_3_1·b_3_3 + b_2_03·b_3_0·b_3_5
       + b_2_03·b_3_0·b_3_4 + b_2_03·b_3_0·b_3_3 + b_2_03·b_3_0·b_3_2 + b_2_03·b_3_0·b_3_1
       + b_2_03·b_3_02 + b_2_03·b_6_19 + b_2_03·b_6_7 + b_2_05·b_2_1 + c_12_74 + c_12_73
       + b_2_0·b_2_1·c_8_32 + b_2_02·c_8_32
  18. c_12_0 → b_3_23·b_3_3 + b_3_03·b_3_3 + b_3_03·b_3_2 + b_6_18·b_3_02 + b_6_18·b_6_19
       + b_6_7·b_3_2·b_3_5 + b_6_7·b_3_2·b_3_4 + b_6_7·b_3_1·b_3_5 + b_6_7·b_3_1·b_3_4
       + b_6_7·b_3_12 + b_6_7·b_3_0·b_3_4 + b_6_7·b_3_0·b_3_3 + b_6_7·b_3_0·b_3_1
       + b_2_0·b_5_8·b_5_9 + b_2_0·b_5_82 + b_2_02·b_3_2·b_5_8 + b_2_02·b_3_1·b_5_12
       + b_2_02·b_3_1·b_5_11 + b_2_02·b_3_1·b_5_8 + b_2_02·b_3_0·b_5_9
       + b_2_03·b_3_2·b_3_5 + b_2_03·b_3_22 + b_2_03·b_3_1·b_3_5 + b_2_03·b_3_1·b_3_4
       + b_2_03·b_3_1·b_3_2 + b_2_03·b_3_12 + b_2_03·b_3_02 + b_2_03·b_6_18
       + b_2_03·b_6_7 + b_2_06 + c_12_74 + b_2_0·b_2_1·c_8_32 + b_2_02·c_8_32

Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 2

  1. a_2_1 → 0, an element of degree 2
  2. a_2_0 → 0, an element of degree 2
  3. b_3_1 → 0, an element of degree 3
  4. b_3_0 → 0, an element of degree 3
  5. b_5_3 → 0, an element of degree 5
  6. b_5_2 → 0, an element of degree 5
  7. b_5_1 → 0, an element of degree 5
  8. b_5_0 → 0, an element of degree 5
  9. b_6_5 → 0, an element of degree 6
  10. b_6_3 → 0, an element of degree 6
  11. b_6_0 → 0, an element of degree 6
  12. c_8_8 → c_1_18 + c_1_04·c_1_14 + c_1_08, an element of degree 8
  13. b_9_3 → 0, an element of degree 9
  14. b_9_2 → 0, an element of degree 9
  15. b_9_1 → 0, an element of degree 9
  16. b_9_0 → 0, an element of degree 9
  17. c_12_1 → c_1_112 + c_1_08·c_1_14 + c_1_012, an element of degree 12
  18. c_12_0 → c_1_04·c_1_18 + c_1_08·c_1_14, an element of degree 12

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

  1. a_2_1 → 0, an element of degree 2
  2. a_2_0 → 0, an element of degree 2
  3. b_3_1 → c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_22 + c_1_02·c_1_2, an element of degree 3
  4. b_3_0 → c_1_1·c_1_22 + c_1_12·c_1_2 + c_1_0·c_1_32 + c_1_0·c_1_22 + c_1_02·c_1_3
       + c_1_02·c_1_2, an element of degree 3
  5. b_5_3 → 0, an element of degree 5
  6. b_5_2 → 0, an element of degree 5
  7. b_5_1 → c_1_1·c_1_34 + c_1_1·c_1_24 + c_1_14·c_1_3 + c_1_14·c_1_2 + c_1_0·c_1_34
       + c_1_04·c_1_3, an element of degree 5
  8. b_5_0 → c_1_1·c_1_34 + c_1_14·c_1_3 + c_1_0·c_1_24 + c_1_04·c_1_2, an element of degree 5
  9. b_6_5 → c_1_12·c_1_34 + c_1_12·c_1_24 + c_1_14·c_1_32 + c_1_14·c_1_22
       + c_1_02·c_1_34 + c_1_04·c_1_32, an element of degree 6
  10. b_6_3 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_02·c_1_34 + c_1_02·c_1_24
       + c_1_04·c_1_32 + c_1_04·c_1_22, an element of degree 6
  11. b_6_0 → c_1_12·c_1_34 + c_1_12·c_1_24 + c_1_14·c_1_32 + c_1_14·c_1_22
       + c_1_02·c_1_34 + c_1_04·c_1_32, an element of degree 6
  12. c_8_8 → c_1_38 + c_1_24·c_1_34 + c_1_28 + c_1_12·c_1_36 + c_1_13·c_1_35
       + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_24·c_1_3 + c_1_14·c_1_34
       + c_1_14·c_1_22·c_1_32 + c_1_14·c_1_24 + c_1_15·c_1_33
       + c_1_15·c_1_2·c_1_32 + c_1_15·c_1_22·c_1_3 + c_1_16·c_1_32 + c_1_18
       + c_1_0·c_1_1·c_1_22·c_1_34 + c_1_0·c_1_1·c_1_24·c_1_32
       + c_1_0·c_1_12·c_1_35 + c_1_0·c_1_12·c_1_2·c_1_34 + c_1_0·c_1_12·c_1_24·c_1_3
       + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_33 + c_1_0·c_1_14·c_1_2·c_1_32
       + c_1_0·c_1_14·c_1_22·c_1_3 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_26
       + c_1_02·c_1_1·c_1_35 + c_1_02·c_1_1·c_1_2·c_1_34 + c_1_02·c_1_1·c_1_24·c_1_3
       + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_34
       + c_1_02·c_1_12·c_1_22·c_1_32 + c_1_02·c_1_12·c_1_24
       + c_1_02·c_1_14·c_1_2·c_1_3 + c_1_03·c_1_2·c_1_34 + c_1_03·c_1_24·c_1_3
       + c_1_03·c_1_25 + c_1_04·c_1_34 + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_24
       + c_1_04·c_1_1·c_1_33 + c_1_04·c_1_1·c_1_2·c_1_32 + c_1_04·c_1_1·c_1_22·c_1_3
       + c_1_04·c_1_1·c_1_23 + c_1_04·c_1_12·c_1_2·c_1_3 + c_1_04·c_1_14
       + c_1_05·c_1_2·c_1_32 + c_1_05·c_1_22·c_1_3 + c_1_05·c_1_23 + c_1_06·c_1_22
       + c_1_08, an element of degree 8
  13. b_9_3 → c_1_13·c_1_24·c_1_32 + c_1_13·c_1_26 + c_1_14·c_1_24·c_1_3 + c_1_14·c_1_25
       + c_1_15·c_1_22·c_1_32 + c_1_15·c_1_24 + c_1_16·c_1_22·c_1_3
       + c_1_16·c_1_23 + c_1_0·c_1_12·c_1_24·c_1_32 + c_1_0·c_1_14·c_1_22·c_1_32
       + c_1_02·c_1_1·c_1_36 + c_1_02·c_1_1·c_1_22·c_1_34
       + c_1_02·c_1_1·c_1_24·c_1_32 + c_1_02·c_1_1·c_1_26 + c_1_02·c_1_12·c_1_35
       + c_1_02·c_1_12·c_1_2·c_1_34 + c_1_02·c_1_12·c_1_25
       + c_1_02·c_1_14·c_1_22·c_1_3 + c_1_03·c_1_36 + c_1_03·c_1_24·c_1_32
       + c_1_04·c_1_35 + c_1_04·c_1_24·c_1_3 + c_1_04·c_1_1·c_1_34
       + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_12·c_1_33 + c_1_04·c_1_12·c_1_2·c_1_32
       + c_1_04·c_1_12·c_1_22·c_1_3 + c_1_04·c_1_12·c_1_23 + c_1_05·c_1_34
       + c_1_05·c_1_22·c_1_32 + c_1_06·c_1_33 + c_1_06·c_1_22·c_1_3, an element of degree 9
  14. b_9_2 → c_1_13·c_1_22·c_1_34 + c_1_13·c_1_24·c_1_32 + c_1_13·c_1_26
       + c_1_14·c_1_2·c_1_34 + c_1_14·c_1_24·c_1_3 + c_1_14·c_1_25 + c_1_15·c_1_24
       + c_1_16·c_1_2·c_1_32 + c_1_16·c_1_22·c_1_3 + c_1_16·c_1_23
       + c_1_0·c_1_12·c_1_36 + c_1_0·c_1_12·c_1_22·c_1_34
       + c_1_0·c_1_12·c_1_24·c_1_32 + c_1_0·c_1_14·c_1_34 + c_1_02·c_1_1·c_1_36
       + c_1_02·c_1_1·c_1_22·c_1_34 + c_1_02·c_1_1·c_1_24·c_1_32
       + c_1_02·c_1_14·c_1_33 + c_1_02·c_1_14·c_1_2·c_1_32
       + c_1_02·c_1_14·c_1_22·c_1_3 + c_1_03·c_1_36 + c_1_03·c_1_26
       + c_1_04·c_1_35 + c_1_04·c_1_25 + c_1_04·c_1_1·c_1_34
       + c_1_04·c_1_12·c_1_33 + c_1_04·c_1_12·c_1_2·c_1_32
       + c_1_04·c_1_12·c_1_22·c_1_3 + c_1_05·c_1_34 + c_1_05·c_1_24
       + c_1_06·c_1_33 + c_1_06·c_1_23, an element of degree 9
  15. b_9_1 → c_1_1·c_1_38 + c_1_1·c_1_28 + c_1_13·c_1_36 + c_1_13·c_1_26 + c_1_14·c_1_35
       + c_1_14·c_1_25 + c_1_15·c_1_34 + c_1_15·c_1_24 + c_1_16·c_1_33
       + c_1_16·c_1_23 + c_1_18·c_1_3 + c_1_18·c_1_2 + c_1_0·c_1_38
       + c_1_0·c_1_12·c_1_22·c_1_34 + c_1_0·c_1_12·c_1_24·c_1_32
       + c_1_0·c_1_12·c_1_26 + c_1_0·c_1_14·c_1_24 + c_1_02·c_1_1·c_1_22·c_1_34
       + c_1_02·c_1_1·c_1_24·c_1_32 + c_1_02·c_1_1·c_1_26
       + c_1_02·c_1_14·c_1_2·c_1_32 + c_1_02·c_1_14·c_1_22·c_1_3
       + c_1_02·c_1_14·c_1_23 + c_1_03·c_1_36 + c_1_03·c_1_22·c_1_34
       + c_1_03·c_1_24·c_1_32 + c_1_04·c_1_35 + c_1_04·c_1_2·c_1_34
       + c_1_04·c_1_24·c_1_3 + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_12·c_1_2·c_1_32
       + c_1_04·c_1_12·c_1_22·c_1_3 + c_1_04·c_1_12·c_1_23 + c_1_05·c_1_34
       + c_1_06·c_1_33 + c_1_06·c_1_2·c_1_32 + c_1_06·c_1_22·c_1_3 + c_1_08·c_1_3, an element of degree 9
  16. b_9_0 → c_1_1·c_1_38 + c_1_18·c_1_3 + c_1_0·c_1_28 + c_1_08·c_1_2, an element of degree 9
  17. c_12_1 → c_1_312 + c_1_28·c_1_34 + c_1_212 + c_1_12·c_1_28·c_1_32 + c_1_13·c_1_39
       + c_1_13·c_1_29 + c_1_14·c_1_24·c_1_34 + c_1_14·c_1_26·c_1_32
       + c_1_15·c_1_25·c_1_32 + c_1_15·c_1_26·c_1_3 + c_1_16·c_1_36
       + c_1_16·c_1_25·c_1_3 + c_1_16·c_1_26 + c_1_17·c_1_23·c_1_32
       + c_1_17·c_1_24·c_1_3 + c_1_18·c_1_22·c_1_32 + c_1_18·c_1_23·c_1_3
       + c_1_19·c_1_33 + c_1_19·c_1_2·c_1_32 + c_1_19·c_1_22·c_1_3 + c_1_19·c_1_23
       + c_1_110·c_1_2·c_1_3 + c_1_112 + c_1_0·c_1_1·c_1_310
       + c_1_0·c_1_1·c_1_28·c_1_32 + c_1_0·c_1_1·c_1_210 + c_1_0·c_1_12·c_1_39
       + c_1_0·c_1_12·c_1_2·c_1_38 + c_1_0·c_1_13·c_1_24·c_1_34
       + c_1_0·c_1_13·c_1_26·c_1_32 + c_1_0·c_1_13·c_1_28
       + c_1_0·c_1_14·c_1_24·c_1_33 + c_1_0·c_1_14·c_1_26·c_1_3
       + c_1_0·c_1_14·c_1_27 + c_1_0·c_1_15·c_1_22·c_1_34
       + c_1_0·c_1_15·c_1_24·c_1_32 + c_1_0·c_1_15·c_1_26
       + c_1_0·c_1_16·c_1_22·c_1_33 + c_1_0·c_1_16·c_1_24·c_1_3
       + c_1_0·c_1_16·c_1_25 + c_1_0·c_1_18·c_1_2·c_1_32 + c_1_0·c_1_18·c_1_22·c_1_3
       + c_1_0·c_1_18·c_1_23 + c_1_02·c_1_22·c_1_38 + c_1_02·c_1_210
       + c_1_02·c_1_1·c_1_39 + c_1_02·c_1_1·c_1_2·c_1_38 + c_1_02·c_1_12·c_1_38
       + c_1_02·c_1_12·c_1_22·c_1_36 + c_1_02·c_1_12·c_1_24·c_1_34
       + c_1_02·c_1_13·c_1_2·c_1_36 + c_1_02·c_1_13·c_1_22·c_1_35
       + c_1_02·c_1_13·c_1_24·c_1_33 + c_1_02·c_1_13·c_1_26·c_1_3
       + c_1_02·c_1_13·c_1_27 + c_1_02·c_1_14·c_1_2·c_1_35
       + c_1_02·c_1_15·c_1_22·c_1_33 + c_1_02·c_1_15·c_1_23·c_1_32
       + c_1_02·c_1_15·c_1_25 + c_1_02·c_1_16·c_1_22·c_1_32
       + c_1_02·c_1_16·c_1_23·c_1_3 + c_1_02·c_1_16·c_1_24 + c_1_02·c_1_18·c_1_22
       + c_1_03·c_1_39 + c_1_03·c_1_2·c_1_38 + c_1_03·c_1_28·c_1_3
       + c_1_03·c_1_1·c_1_38 + c_1_03·c_1_1·c_1_22·c_1_36
       + c_1_03·c_1_1·c_1_26·c_1_32 + c_1_03·c_1_1·c_1_28 + c_1_03·c_1_12·c_1_37
       + c_1_03·c_1_12·c_1_22·c_1_35 + c_1_03·c_1_12·c_1_23·c_1_34
       + c_1_03·c_1_12·c_1_24·c_1_33 + c_1_03·c_1_12·c_1_25·c_1_32
       + c_1_03·c_1_12·c_1_27 + c_1_03·c_1_14·c_1_23·c_1_32
       + c_1_03·c_1_14·c_1_24·c_1_3 + c_1_04·c_1_22·c_1_36 + c_1_04·c_1_26·c_1_32
       + c_1_04·c_1_1·c_1_37 + c_1_04·c_1_1·c_1_2·c_1_36
       + c_1_04·c_1_1·c_1_23·c_1_34 + c_1_04·c_1_1·c_1_24·c_1_33
       + c_1_04·c_1_1·c_1_25·c_1_32 + c_1_04·c_1_1·c_1_27
       + c_1_04·c_1_12·c_1_2·c_1_35 + c_1_04·c_1_12·c_1_24·c_1_32
       + c_1_04·c_1_12·c_1_26 + c_1_04·c_1_13·c_1_2·c_1_34
       + c_1_04·c_1_13·c_1_22·c_1_33 + c_1_04·c_1_13·c_1_23·c_1_32
       + c_1_04·c_1_13·c_1_24·c_1_3 + c_1_04·c_1_14·c_1_34
       + c_1_04·c_1_14·c_1_2·c_1_33 + c_1_04·c_1_14·c_1_22·c_1_32
       + c_1_05·c_1_2·c_1_36 + c_1_05·c_1_22·c_1_35 + c_1_05·c_1_25·c_1_32
       + c_1_05·c_1_26·c_1_3 + c_1_05·c_1_1·c_1_36 + c_1_05·c_1_1·c_1_26
       + c_1_05·c_1_12·c_1_35 + c_1_05·c_1_12·c_1_23·c_1_32
       + c_1_05·c_1_12·c_1_24·c_1_3 + c_1_05·c_1_12·c_1_25 + c_1_06·c_1_36
       + c_1_06·c_1_2·c_1_35 + c_1_06·c_1_24·c_1_32 + c_1_06·c_1_25·c_1_3
       + c_1_06·c_1_26 + c_1_06·c_1_1·c_1_35 + c_1_06·c_1_1·c_1_2·c_1_34
       + c_1_06·c_1_1·c_1_22·c_1_33 + c_1_06·c_1_1·c_1_25 + c_1_06·c_1_12·c_1_34
       + c_1_06·c_1_12·c_1_2·c_1_33 + c_1_06·c_1_12·c_1_23·c_1_3
       + c_1_06·c_1_12·c_1_24 + c_1_07·c_1_2·c_1_34 + c_1_07·c_1_22·c_1_33
       + c_1_07·c_1_23·c_1_32 + c_1_07·c_1_24·c_1_3 + c_1_08·c_1_2·c_1_33
       + c_1_08·c_1_23·c_1_3 + c_1_08·c_1_1·c_1_23 + c_1_08·c_1_12·c_1_32
       + c_1_08·c_1_12·c_1_2·c_1_3 + c_1_08·c_1_14 + c_1_09·c_1_33
       + c_1_010·c_1_2·c_1_3 + c_1_010·c_1_22 + c_1_012, an element of degree 12
  18. c_12_0 → c_1_24·c_1_38 + c_1_28·c_1_34 + c_1_12·c_1_310 + c_1_13·c_1_39
       + c_1_13·c_1_2·c_1_38 + c_1_13·c_1_28·c_1_3 + c_1_14·c_1_24·c_1_34
       + c_1_14·c_1_26·c_1_32 + c_1_15·c_1_25·c_1_32 + c_1_15·c_1_26·c_1_3
       + c_1_16·c_1_24·c_1_32 + c_1_16·c_1_25·c_1_3 + c_1_17·c_1_23·c_1_32
       + c_1_17·c_1_24·c_1_3 + c_1_18·c_1_22·c_1_32 + c_1_18·c_1_23·c_1_3
       + c_1_19·c_1_33 + c_1_19·c_1_2·c_1_32 + c_1_19·c_1_22·c_1_3 + c_1_110·c_1_32
       + c_1_0·c_1_1·c_1_22·c_1_38 + c_1_0·c_1_1·c_1_28·c_1_32
       + c_1_0·c_1_12·c_1_39 + c_1_0·c_1_12·c_1_2·c_1_38 + c_1_0·c_1_12·c_1_28·c_1_3
       + c_1_0·c_1_12·c_1_29 + c_1_0·c_1_13·c_1_24·c_1_34
       + c_1_0·c_1_13·c_1_26·c_1_32 + c_1_0·c_1_13·c_1_28
       + c_1_0·c_1_14·c_1_24·c_1_33 + c_1_0·c_1_14·c_1_26·c_1_3
       + c_1_0·c_1_14·c_1_27 + c_1_0·c_1_15·c_1_22·c_1_34
       + c_1_0·c_1_15·c_1_24·c_1_32 + c_1_0·c_1_15·c_1_26
       + c_1_0·c_1_16·c_1_22·c_1_33 + c_1_0·c_1_16·c_1_24·c_1_3
       + c_1_0·c_1_16·c_1_25 + c_1_0·c_1_18·c_1_33 + c_1_0·c_1_18·c_1_2·c_1_32
       + c_1_0·c_1_18·c_1_22·c_1_3 + c_1_0·c_1_18·c_1_23 + c_1_02·c_1_210
       + c_1_02·c_1_1·c_1_39 + c_1_02·c_1_1·c_1_2·c_1_38 + c_1_02·c_1_1·c_1_28·c_1_3
       + c_1_02·c_1_1·c_1_29 + c_1_02·c_1_12·c_1_38
       + c_1_02·c_1_12·c_1_22·c_1_36 + c_1_02·c_1_12·c_1_24·c_1_34
       + c_1_02·c_1_13·c_1_2·c_1_36 + c_1_02·c_1_13·c_1_22·c_1_35
       + c_1_02·c_1_13·c_1_24·c_1_33 + c_1_02·c_1_13·c_1_26·c_1_3
       + c_1_02·c_1_13·c_1_27 + c_1_02·c_1_14·c_1_2·c_1_35
       + c_1_02·c_1_14·c_1_22·c_1_34 + c_1_02·c_1_14·c_1_24·c_1_32
       + c_1_02·c_1_15·c_1_22·c_1_33 + c_1_02·c_1_15·c_1_23·c_1_32
       + c_1_02·c_1_15·c_1_25 + c_1_02·c_1_16·c_1_22·c_1_32
       + c_1_02·c_1_16·c_1_23·c_1_3 + c_1_02·c_1_16·c_1_24
       + c_1_02·c_1_18·c_1_2·c_1_3 + c_1_03·c_1_2·c_1_38 + c_1_03·c_1_28·c_1_3
       + c_1_03·c_1_29 + c_1_03·c_1_1·c_1_38 + c_1_03·c_1_1·c_1_22·c_1_36
       + c_1_03·c_1_1·c_1_26·c_1_32 + c_1_03·c_1_1·c_1_28 + c_1_03·c_1_12·c_1_37
       + c_1_03·c_1_12·c_1_22·c_1_35 + c_1_03·c_1_12·c_1_23·c_1_34
       + c_1_03·c_1_12·c_1_24·c_1_33 + c_1_03·c_1_12·c_1_25·c_1_32
       + c_1_03·c_1_12·c_1_27 + c_1_03·c_1_14·c_1_23·c_1_32
       + c_1_03·c_1_14·c_1_24·c_1_3 + c_1_04·c_1_22·c_1_36 + c_1_04·c_1_26·c_1_32
       + c_1_04·c_1_1·c_1_37 + c_1_04·c_1_1·c_1_2·c_1_36
       + c_1_04·c_1_1·c_1_23·c_1_34 + c_1_04·c_1_1·c_1_24·c_1_33
       + c_1_04·c_1_1·c_1_25·c_1_32 + c_1_04·c_1_1·c_1_27 + c_1_04·c_1_12·c_1_36
       + c_1_04·c_1_12·c_1_2·c_1_35 + c_1_04·c_1_12·c_1_22·c_1_34
       + c_1_04·c_1_12·c_1_24·c_1_32 + c_1_04·c_1_13·c_1_2·c_1_34
       + c_1_04·c_1_13·c_1_22·c_1_33 + c_1_04·c_1_13·c_1_23·c_1_32
       + c_1_04·c_1_13·c_1_24·c_1_3 + c_1_04·c_1_14·c_1_34
       + c_1_04·c_1_14·c_1_2·c_1_33 + c_1_04·c_1_14·c_1_22·c_1_32
       + c_1_04·c_1_18 + c_1_05·c_1_2·c_1_36 + c_1_05·c_1_22·c_1_35
       + c_1_05·c_1_25·c_1_32 + c_1_05·c_1_26·c_1_3 + c_1_05·c_1_1·c_1_36
       + c_1_05·c_1_1·c_1_26 + c_1_05·c_1_12·c_1_35
       + c_1_05·c_1_12·c_1_23·c_1_32 + c_1_05·c_1_12·c_1_24·c_1_3
       + c_1_05·c_1_12·c_1_25 + c_1_06·c_1_2·c_1_35 + c_1_06·c_1_25·c_1_3
       + c_1_06·c_1_1·c_1_35 + c_1_06·c_1_1·c_1_2·c_1_34
       + c_1_06·c_1_1·c_1_22·c_1_33 + c_1_06·c_1_1·c_1_25 + c_1_06·c_1_12·c_1_34
       + c_1_06·c_1_12·c_1_2·c_1_33 + c_1_06·c_1_12·c_1_23·c_1_3
       + c_1_06·c_1_12·c_1_24 + c_1_07·c_1_2·c_1_34 + c_1_07·c_1_22·c_1_33
       + c_1_07·c_1_23·c_1_32 + c_1_07·c_1_24·c_1_3 + c_1_08·c_1_2·c_1_33
       + c_1_08·c_1_23·c_1_3 + c_1_08·c_1_1·c_1_33 + c_1_08·c_1_1·c_1_2·c_1_32
       + c_1_08·c_1_1·c_1_22·c_1_3 + c_1_08·c_1_1·c_1_23 + c_1_08·c_1_12·c_1_2·c_1_3
       + c_1_08·c_1_14 + c_1_09·c_1_2·c_1_32 + c_1_09·c_1_22·c_1_3 + c_1_09·c_1_23
       + c_1_010·c_1_22, an element of degree 12

Restriction map to a maximal el. ab. subgp. of rank 4 in a Sylow subgroup

  1. a_2_1 → 0, an element of degree 2
  2. a_2_0 → 0, an element of degree 2
  3. b_3_1 → c_1_1·c_1_32 + c_1_1·c_1_22 + c_1_12·c_1_3 + c_1_12·c_1_2 + c_1_0·c_1_32
       + c_1_02·c_1_3, an element of degree 3
  4. b_3_0 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_22 + c_1_12·c_1_2 + c_1_0·c_1_32
       + c_1_0·c_1_22 + c_1_02·c_1_3 + c_1_02·c_1_2, an element of degree 3
  5. b_5_3 → c_1_2·c_1_34 + c_1_24·c_1_3 + c_1_1·c_1_24 + c_1_14·c_1_2 + c_1_0·c_1_34
       + c_1_0·c_1_24 + c_1_04·c_1_3 + c_1_04·c_1_2, an element of degree 5
  6. b_5_2 → c_1_1·c_1_34 + c_1_1·c_1_24 + c_1_14·c_1_3 + c_1_14·c_1_2 + c_1_0·c_1_34
       + c_1_04·c_1_3, an element of degree 5
  7. b_5_1 → 0, an element of degree 5
  8. b_5_0 → 0, an element of degree 5
  9. b_6_5 → 0, an element of degree 6
  10. b_6_3 → 0, an element of degree 6
  11. b_6_0 → c_1_1·c_1_2·c_1_34 + c_1_1·c_1_22·c_1_33 + c_1_1·c_1_23·c_1_32
       + c_1_1·c_1_24·c_1_3 + c_1_12·c_1_34 + c_1_12·c_1_2·c_1_33
       + c_1_12·c_1_22·c_1_32 + c_1_12·c_1_23·c_1_3 + c_1_13·c_1_2·c_1_32
       + c_1_13·c_1_22·c_1_3 + c_1_14·c_1_32 + c_1_14·c_1_2·c_1_3 + c_1_0·c_1_2·c_1_34
       + c_1_0·c_1_22·c_1_33 + c_1_0·c_1_1·c_1_34 + c_1_0·c_1_1·c_1_22·c_1_32
       + c_1_0·c_1_1·c_1_24 + c_1_0·c_1_12·c_1_33 + c_1_0·c_1_12·c_1_22·c_1_3
       + c_1_0·c_1_12·c_1_23 + c_1_02·c_1_2·c_1_33 + c_1_02·c_1_1·c_1_33
       + c_1_02·c_1_1·c_1_2·c_1_32 + c_1_02·c_1_1·c_1_23 + c_1_02·c_1_12·c_1_32
       + c_1_02·c_1_12·c_1_2·c_1_3 + c_1_02·c_1_12·c_1_22 + c_1_03·c_1_2·c_1_32
       + c_1_03·c_1_22·c_1_3 + c_1_04·c_1_2·c_1_3, an element of degree 6
  12. c_8_8 → c_1_38 + c_1_24·c_1_34 + c_1_28 + c_1_1·c_1_2·c_1_36 + c_1_1·c_1_22·c_1_35
       + c_1_1·c_1_25·c_1_32 + c_1_1·c_1_26·c_1_3 + c_1_12·c_1_24·c_1_32
       + c_1_12·c_1_26 + c_1_13·c_1_2·c_1_34 + c_1_13·c_1_25 + c_1_14·c_1_34
       + c_1_14·c_1_2·c_1_33 + c_1_14·c_1_22·c_1_32 + c_1_14·c_1_23·c_1_3
       + c_1_14·c_1_24 + c_1_15·c_1_22·c_1_3 + c_1_15·c_1_23 + c_1_16·c_1_2·c_1_3
       + c_1_16·c_1_22 + c_1_18 + c_1_0·c_1_2·c_1_36 + c_1_0·c_1_22·c_1_35
       + c_1_0·c_1_1·c_1_36 + c_1_0·c_1_1·c_1_22·c_1_34 + c_1_0·c_1_1·c_1_26
       + c_1_0·c_1_12·c_1_24·c_1_3 + c_1_0·c_1_14·c_1_33 + c_1_0·c_1_14·c_1_23
       + c_1_02·c_1_36 + c_1_02·c_1_24·c_1_32 + c_1_02·c_1_1·c_1_35
       + c_1_02·c_1_1·c_1_25 + c_1_02·c_1_12·c_1_34
       + c_1_02·c_1_12·c_1_22·c_1_32 + c_1_02·c_1_12·c_1_24
       + c_1_02·c_1_14·c_1_2·c_1_3 + c_1_03·c_1_35 + c_1_03·c_1_2·c_1_34
       + c_1_04·c_1_34 + c_1_04·c_1_2·c_1_33 + c_1_04·c_1_24
       + c_1_04·c_1_1·c_1_2·c_1_32 + c_1_04·c_1_12·c_1_32 + c_1_04·c_1_12·c_1_22
       + c_1_04·c_1_14 + c_1_05·c_1_33 + c_1_05·c_1_22·c_1_3 + c_1_06·c_1_32
       + c_1_06·c_1_2·c_1_3 + c_1_08, an element of degree 8
  13. b_9_3 → c_1_2·c_1_38 + c_1_28·c_1_3 + c_1_1·c_1_38 + c_1_1·c_1_22·c_1_36
       + c_1_1·c_1_26·c_1_32 + c_1_12·c_1_2·c_1_36 + c_1_12·c_1_23·c_1_34
       + c_1_12·c_1_24·c_1_33 + c_1_12·c_1_26·c_1_3 + c_1_13·c_1_22·c_1_34
       + c_1_13·c_1_24·c_1_32 + c_1_14·c_1_22·c_1_33 + c_1_14·c_1_23·c_1_32
       + c_1_16·c_1_2·c_1_32 + c_1_16·c_1_22·c_1_3 + c_1_18·c_1_3
       + c_1_0·c_1_22·c_1_36 + c_1_0·c_1_24·c_1_34 + c_1_0·c_1_28
       + c_1_0·c_1_12·c_1_36 + c_1_0·c_1_12·c_1_22·c_1_34 + c_1_0·c_1_12·c_1_26
       + c_1_0·c_1_14·c_1_34 + c_1_0·c_1_14·c_1_22·c_1_32 + c_1_0·c_1_14·c_1_24
       + c_1_02·c_1_2·c_1_36 + c_1_02·c_1_24·c_1_33 + c_1_02·c_1_1·c_1_36
       + c_1_02·c_1_1·c_1_24·c_1_32 + c_1_02·c_1_1·c_1_26
       + c_1_02·c_1_12·c_1_2·c_1_34 + c_1_02·c_1_12·c_1_24·c_1_3
       + c_1_02·c_1_14·c_1_33 + c_1_02·c_1_14·c_1_2·c_1_32
       + c_1_02·c_1_14·c_1_23 + c_1_03·c_1_22·c_1_34 + c_1_03·c_1_24·c_1_32
       + c_1_04·c_1_22·c_1_33 + c_1_04·c_1_24·c_1_3 + c_1_04·c_1_1·c_1_34
       + c_1_04·c_1_1·c_1_22·c_1_32 + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_12·c_1_33
       + c_1_04·c_1_12·c_1_22·c_1_3 + c_1_04·c_1_12·c_1_23 + c_1_06·c_1_2·c_1_32
       + c_1_06·c_1_22·c_1_3 + c_1_08·c_1_2, an element of degree 9
  14. b_9_2 → c_1_2·c_1_38 + c_1_28·c_1_3 + c_1_1·c_1_22·c_1_36 + c_1_1·c_1_26·c_1_32
       + c_1_1·c_1_28 + c_1_12·c_1_22·c_1_35 + c_1_12·c_1_23·c_1_34
       + c_1_12·c_1_24·c_1_33 + c_1_12·c_1_25·c_1_32 + c_1_13·c_1_24·c_1_32
       + c_1_13·c_1_26 + c_1_14·c_1_24·c_1_3 + c_1_14·c_1_25
       + c_1_15·c_1_22·c_1_32 + c_1_15·c_1_24 + c_1_16·c_1_22·c_1_3
       + c_1_16·c_1_23 + c_1_18·c_1_2 + c_1_0·c_1_38 + c_1_0·c_1_22·c_1_36
       + c_1_0·c_1_24·c_1_34 + c_1_0·c_1_28 + c_1_0·c_1_12·c_1_24·c_1_32
       + c_1_0·c_1_14·c_1_22·c_1_32 + c_1_02·c_1_22·c_1_35
       + c_1_02·c_1_24·c_1_33 + c_1_02·c_1_1·c_1_36 + c_1_02·c_1_1·c_1_22·c_1_34
       + c_1_02·c_1_1·c_1_24·c_1_32 + c_1_02·c_1_1·c_1_26 + c_1_02·c_1_12·c_1_35
       + c_1_02·c_1_12·c_1_2·c_1_34 + c_1_02·c_1_12·c_1_25
       + c_1_02·c_1_14·c_1_22·c_1_3 + c_1_03·c_1_36 + c_1_03·c_1_24·c_1_32
       + c_1_04·c_1_35 + c_1_04·c_1_24·c_1_3 + c_1_04·c_1_1·c_1_34
       + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_12·c_1_33 + c_1_04·c_1_12·c_1_2·c_1_32
       + c_1_04·c_1_12·c_1_22·c_1_3 + c_1_04·c_1_12·c_1_23 + c_1_05·c_1_34
       + c_1_05·c_1_22·c_1_32 + c_1_06·c_1_33 + c_1_06·c_1_22·c_1_3 + c_1_08·c_1_3
       + c_1_08·c_1_2, an element of degree 9
  15. b_9_1 → 0, an element of degree 9
  16. b_9_0 → 0, an element of degree 9
  17. c_12_1 → c_1_312 + c_1_22·c_1_310 + c_1_24·c_1_38 + c_1_26·c_1_36 + c_1_28·c_1_34
       + c_1_210·c_1_32 + c_1_212 + c_1_1·c_1_22·c_1_39 + c_1_1·c_1_23·c_1_38
       + c_1_1·c_1_28·c_1_33 + c_1_1·c_1_29·c_1_32 + c_1_12·c_1_310
       + c_1_12·c_1_22·c_1_38 + c_1_12·c_1_24·c_1_36 + c_1_13·c_1_2·c_1_38
       + c_1_13·c_1_22·c_1_37 + c_1_13·c_1_23·c_1_36 + c_1_13·c_1_24·c_1_35
       + c_1_13·c_1_25·c_1_34 + c_1_13·c_1_26·c_1_33 + c_1_13·c_1_27·c_1_32
       + c_1_13·c_1_29 + c_1_14·c_1_2·c_1_37 + c_1_14·c_1_22·c_1_36
       + c_1_14·c_1_23·c_1_35 + c_1_14·c_1_25·c_1_33 + c_1_14·c_1_27·c_1_3
       + c_1_16·c_1_36 + c_1_16·c_1_22·c_1_34 + c_1_16·c_1_26
       + c_1_17·c_1_2·c_1_34 + c_1_17·c_1_22·c_1_33 + c_1_17·c_1_23·c_1_32
       + c_1_17·c_1_24·c_1_3 + c_1_18·c_1_2·c_1_33 + c_1_18·c_1_22·c_1_32
       + c_1_18·c_1_23·c_1_3 + c_1_19·c_1_22·c_1_3 + c_1_19·c_1_23 + c_1_110·c_1_32
       + c_1_112 + c_1_0·c_1_22·c_1_39 + c_1_0·c_1_28·c_1_33
       + c_1_0·c_1_1·c_1_22·c_1_38 + c_1_0·c_1_1·c_1_28·c_1_32
       + c_1_0·c_1_12·c_1_22·c_1_37 + c_1_0·c_1_12·c_1_25·c_1_34
       + c_1_0·c_1_12·c_1_26·c_1_33 + c_1_0·c_1_13·c_1_38
       + c_1_0·c_1_13·c_1_22·c_1_36 + c_1_0·c_1_13·c_1_26·c_1_32
       + c_1_0·c_1_13·c_1_28 + c_1_0·c_1_14·c_1_37 + c_1_0·c_1_14·c_1_2·c_1_36
       + c_1_0·c_1_14·c_1_26·c_1_3 + c_1_0·c_1_14·c_1_27 + c_1_0·c_1_15·c_1_36
       + c_1_0·c_1_15·c_1_26 + c_1_0·c_1_16·c_1_35 + c_1_0·c_1_16·c_1_23·c_1_32
       + c_1_0·c_1_16·c_1_24·c_1_3 + c_1_0·c_1_16·c_1_25 + c_1_0·c_1_18·c_1_2·c_1_32
       + c_1_02·c_1_26·c_1_34 + c_1_02·c_1_28·c_1_32 + c_1_02·c_1_210
       + c_1_02·c_1_1·c_1_39 + c_1_02·c_1_1·c_1_2·c_1_38
       + c_1_02·c_1_1·c_1_22·c_1_37 + c_1_02·c_1_1·c_1_23·c_1_36
       + c_1_02·c_1_1·c_1_24·c_1_35 + c_1_02·c_1_1·c_1_29 + c_1_02·c_1_12·c_1_38
       + c_1_02·c_1_12·c_1_22·c_1_36 + c_1_02·c_1_12·c_1_23·c_1_35
       + c_1_02·c_1_12·c_1_25·c_1_33 + c_1_02·c_1_13·c_1_37
       + c_1_02·c_1_13·c_1_22·c_1_35 + c_1_02·c_1_13·c_1_23·c_1_34
       + c_1_02·c_1_13·c_1_24·c_1_33 + c_1_02·c_1_13·c_1_25·c_1_32
       + c_1_02·c_1_13·c_1_27 + c_1_02·c_1_14·c_1_36
       + c_1_02·c_1_14·c_1_2·c_1_35 + c_1_02·c_1_14·c_1_22·c_1_34
       + c_1_02·c_1_14·c_1_23·c_1_33 + c_1_02·c_1_14·c_1_25·c_1_3
       + c_1_02·c_1_15·c_1_35 + c_1_02·c_1_15·c_1_2·c_1_34
       + c_1_02·c_1_15·c_1_22·c_1_33 + c_1_02·c_1_15·c_1_25
       + c_1_02·c_1_16·c_1_34 + c_1_02·c_1_16·c_1_2·c_1_33
       + c_1_02·c_1_16·c_1_23·c_1_3 + c_1_02·c_1_16·c_1_24
       + c_1_02·c_1_18·c_1_2·c_1_3 + c_1_03·c_1_39 + c_1_03·c_1_2·c_1_38
       + c_1_03·c_1_22·c_1_37 + c_1_03·c_1_28·c_1_3 + c_1_03·c_1_1·c_1_38
       + c_1_03·c_1_1·c_1_22·c_1_36 + c_1_03·c_1_1·c_1_24·c_1_34
       + c_1_03·c_1_12·c_1_37 + c_1_03·c_1_12·c_1_2·c_1_36
       + c_1_03·c_1_12·c_1_23·c_1_34 + c_1_03·c_1_12·c_1_25·c_1_32
       + c_1_03·c_1_12·c_1_26·c_1_3 + c_1_03·c_1_14·c_1_2·c_1_34
       + c_1_03·c_1_14·c_1_22·c_1_33 + c_1_03·c_1_14·c_1_23·c_1_32
       + c_1_03·c_1_14·c_1_24·c_1_3 + c_1_04·c_1_2·c_1_37 + c_1_04·c_1_22·c_1_36
       + c_1_04·c_1_26·c_1_32 + c_1_04·c_1_28 + c_1_04·c_1_1·c_1_37
       + c_1_04·c_1_1·c_1_22·c_1_35 + c_1_04·c_1_1·c_1_24·c_1_33
       + c_1_04·c_1_12·c_1_2·c_1_35 + c_1_04·c_1_12·c_1_22·c_1_34
       + c_1_04·c_1_12·c_1_23·c_1_33 + c_1_04·c_1_12·c_1_24·c_1_32
       + c_1_04·c_1_12·c_1_25·c_1_3 + c_1_04·c_1_13·c_1_2·c_1_34
       + c_1_04·c_1_13·c_1_22·c_1_33 + c_1_04·c_1_14·c_1_34
       + c_1_04·c_1_14·c_1_23·c_1_3 + c_1_05·c_1_1·c_1_36
       + c_1_05·c_1_1·c_1_22·c_1_34 + c_1_05·c_1_1·c_1_24·c_1_32
       + c_1_05·c_1_12·c_1_35 + c_1_05·c_1_12·c_1_22·c_1_33
       + c_1_05·c_1_12·c_1_23·c_1_32 + c_1_06·c_1_36 + c_1_06·c_1_22·c_1_34
       + c_1_06·c_1_26 + c_1_06·c_1_1·c_1_35 + c_1_06·c_1_1·c_1_2·c_1_34
       + c_1_06·c_1_1·c_1_23·c_1_32 + c_1_06·c_1_12·c_1_34
       + c_1_06·c_1_12·c_1_2·c_1_33 + c_1_06·c_1_12·c_1_22·c_1_32
       + c_1_07·c_1_2·c_1_34 + c_1_07·c_1_22·c_1_33 + c_1_08·c_1_2·c_1_33
       + c_1_08·c_1_24 + c_1_08·c_1_1·c_1_33 + c_1_08·c_1_1·c_1_23
       + c_1_08·c_1_12·c_1_2·c_1_3 + c_1_08·c_1_14 + c_1_09·c_1_33
       + c_1_09·c_1_22·c_1_3 + c_1_010·c_1_22 + c_1_012, an element of degree 12
  18. c_12_0 → c_1_24·c_1_38 + c_1_28·c_1_34 + c_1_1·c_1_2·c_1_310 + c_1_1·c_1_24·c_1_37
       + c_1_1·c_1_27·c_1_34 + c_1_1·c_1_210·c_1_3 + c_1_12·c_1_310
       + c_1_12·c_1_2·c_1_39 + c_1_12·c_1_22·c_1_38 + c_1_12·c_1_23·c_1_37
       + c_1_12·c_1_24·c_1_36 + c_1_12·c_1_27·c_1_33 + c_1_12·c_1_28·c_1_32
       + c_1_12·c_1_29·c_1_3 + c_1_13·c_1_39 + c_1_13·c_1_22·c_1_37
       + c_1_13·c_1_25·c_1_34 + c_1_13·c_1_26·c_1_33 + c_1_14·c_1_2·c_1_37
       + c_1_14·c_1_22·c_1_36 + c_1_14·c_1_24·c_1_34 + c_1_14·c_1_25·c_1_33
       + c_1_14·c_1_26·c_1_32 + c_1_15·c_1_23·c_1_34 + c_1_15·c_1_24·c_1_33
       + c_1_16·c_1_23·c_1_33 + c_1_16·c_1_24·c_1_32 + c_1_17·c_1_2·c_1_34
       + c_1_17·c_1_22·c_1_33 + c_1_18·c_1_2·c_1_33 + c_1_19·c_1_33
       + c_1_19·c_1_22·c_1_3 + c_1_110·c_1_32 + c_1_110·c_1_2·c_1_3
       + c_1_0·c_1_2·c_1_310 + c_1_0·c_1_23·c_1_38 + c_1_0·c_1_24·c_1_37
       + c_1_0·c_1_25·c_1_36 + c_1_0·c_1_26·c_1_35 + c_1_0·c_1_28·c_1_33
       + c_1_0·c_1_1·c_1_310 + c_1_0·c_1_1·c_1_28·c_1_32 + c_1_0·c_1_1·c_1_210
       + c_1_0·c_1_12·c_1_25·c_1_34 + c_1_0·c_1_12·c_1_26·c_1_33
       + c_1_0·c_1_12·c_1_27·c_1_32 + c_1_0·c_1_12·c_1_29 + c_1_0·c_1_13·c_1_38
       + c_1_0·c_1_13·c_1_22·c_1_36 + c_1_0·c_1_13·c_1_24·c_1_34
       + c_1_0·c_1_14·c_1_37 + c_1_0·c_1_14·c_1_2·c_1_36
       + c_1_0·c_1_14·c_1_23·c_1_34 + c_1_0·c_1_15·c_1_36
       + c_1_0·c_1_15·c_1_22·c_1_34 + c_1_0·c_1_15·c_1_24·c_1_32
       + c_1_0·c_1_16·c_1_35 + c_1_0·c_1_16·c_1_22·c_1_33
       + c_1_0·c_1_16·c_1_23·c_1_32 + c_1_0·c_1_18·c_1_33
       + c_1_0·c_1_18·c_1_2·c_1_32 + c_1_0·c_1_18·c_1_22·c_1_3 + c_1_02·c_1_2·c_1_39
       + c_1_02·c_1_23·c_1_37 + c_1_02·c_1_24·c_1_36 + c_1_02·c_1_25·c_1_35
       + c_1_02·c_1_28·c_1_32 + c_1_02·c_1_1·c_1_39 + c_1_02·c_1_1·c_1_2·c_1_38
       + c_1_02·c_1_1·c_1_22·c_1_37 + c_1_02·c_1_1·c_1_23·c_1_36
       + c_1_02·c_1_1·c_1_24·c_1_35 + c_1_02·c_1_1·c_1_25·c_1_34
       + c_1_02·c_1_1·c_1_26·c_1_33 + c_1_02·c_1_12·c_1_2·c_1_37
       + c_1_02·c_1_12·c_1_22·c_1_36 + c_1_02·c_1_12·c_1_23·c_1_35
       + c_1_02·c_1_12·c_1_24·c_1_34 + c_1_02·c_1_12·c_1_27·c_1_3
       + c_1_02·c_1_13·c_1_37 + c_1_02·c_1_13·c_1_2·c_1_36
       + c_1_02·c_1_13·c_1_23·c_1_34 + c_1_02·c_1_13·c_1_25·c_1_32
       + c_1_02·c_1_13·c_1_26·c_1_3 + c_1_02·c_1_14·c_1_24·c_1_32
       + c_1_02·c_1_14·c_1_25·c_1_3 + c_1_02·c_1_14·c_1_26 + c_1_02·c_1_15·c_1_35
       + c_1_02·c_1_15·c_1_2·c_1_34 + c_1_02·c_1_15·c_1_23·c_1_32
       + c_1_02·c_1_16·c_1_34 + c_1_02·c_1_16·c_1_2·c_1_33
       + c_1_02·c_1_16·c_1_22·c_1_32 + c_1_02·c_1_18·c_1_2·c_1_3
       + c_1_02·c_1_18·c_1_22 + c_1_03·c_1_23·c_1_36 + c_1_03·c_1_24·c_1_35
       + c_1_03·c_1_28·c_1_3 + c_1_03·c_1_1·c_1_24·c_1_34
       + c_1_03·c_1_1·c_1_26·c_1_32 + c_1_03·c_1_1·c_1_28
       + c_1_03·c_1_12·c_1_2·c_1_36 + c_1_03·c_1_12·c_1_22·c_1_35
       + c_1_03·c_1_12·c_1_24·c_1_33 + c_1_03·c_1_12·c_1_26·c_1_3
       + c_1_03·c_1_12·c_1_27 + c_1_03·c_1_14·c_1_2·c_1_34
       + c_1_03·c_1_14·c_1_22·c_1_33 + c_1_04·c_1_22·c_1_36
       + c_1_04·c_1_23·c_1_35 + c_1_04·c_1_24·c_1_34 + c_1_04·c_1_28
       + c_1_04·c_1_1·c_1_23·c_1_34 + c_1_04·c_1_1·c_1_26·c_1_3
       + c_1_04·c_1_1·c_1_27 + c_1_04·c_1_12·c_1_36 + c_1_04·c_1_12·c_1_2·c_1_35
       + c_1_04·c_1_12·c_1_22·c_1_34 + c_1_04·c_1_12·c_1_23·c_1_33
       + c_1_04·c_1_12·c_1_24·c_1_32 + c_1_04·c_1_13·c_1_23·c_1_32
       + c_1_04·c_1_13·c_1_24·c_1_3 + c_1_04·c_1_14·c_1_2·c_1_33
       + c_1_04·c_1_14·c_1_22·c_1_32 + c_1_04·c_1_14·c_1_23·c_1_3 + c_1_04·c_1_18
       + c_1_05·c_1_23·c_1_34 + c_1_05·c_1_24·c_1_33 + c_1_05·c_1_25·c_1_32
       + c_1_05·c_1_26·c_1_3 + c_1_05·c_1_1·c_1_22·c_1_34
       + c_1_05·c_1_1·c_1_24·c_1_32 + c_1_05·c_1_1·c_1_26
       + c_1_05·c_1_12·c_1_22·c_1_33 + c_1_05·c_1_12·c_1_24·c_1_3
       + c_1_05·c_1_12·c_1_25 + c_1_06·c_1_22·c_1_34 + c_1_06·c_1_23·c_1_33
       + c_1_06·c_1_24·c_1_32 + c_1_06·c_1_25·c_1_3 + c_1_06·c_1_1·c_1_22·c_1_33
       + c_1_06·c_1_1·c_1_23·c_1_32 + c_1_06·c_1_1·c_1_25
       + c_1_06·c_1_12·c_1_22·c_1_32 + c_1_06·c_1_12·c_1_23·c_1_3
       + c_1_06·c_1_12·c_1_24 + c_1_07·c_1_23·c_1_32 + c_1_07·c_1_24·c_1_3
       + c_1_08·c_1_23·c_1_3 + c_1_08·c_1_24 + c_1_08·c_1_1·c_1_22·c_1_3
       + c_1_08·c_1_1·c_1_23 + c_1_08·c_1_12·c_1_32 + c_1_08·c_1_14
       + c_1_09·c_1_2·c_1_32 + c_1_010·c_1_2·c_1_3, an element of degree 12

About the group Ring generators Ring relations Completion information Restriction maps


Simon King
Department of Mathematics and Computer Science
Friedrich-Schiller-Universität Jena
07737 Jena
GERMANY
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46161
Fax: +49 (0)3641 9-46162
Office: Zi. 3529, Ernst-Abbe-Platz 2

Last change: 14.12.2010