Cohomology of group number 138 of order 128

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

General information on the group

  • The group has 2 minimal generators and exponent 8.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 1.
  • It has 2 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 1.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t6  +  t3  +  1)
    (t  +  1) · (t  −  1)3 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-4,-3,-3. They were obtained using the filter regular HSOP of the Benson test.

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring generators

The cohomology ring has 19 minimal generators of maximal degree 9:

  1. a_1_0, a nilpotent element of degree 1
  2. b_1_1, an element of degree 1
  3. a_2_2, a nilpotent element of degree 2
  4. b_2_1, an element of degree 2
  5. b_3_2, an element of degree 3
  6. b_3_3, an element of degree 3
  7. b_3_4, an element of degree 3
  8. b_4_4, an element of degree 4
  9. b_4_6, an element of degree 4
  10. b_5_6, an element of degree 5
  11. b_5_7, an element of degree 5
  12. b_5_8, an element of degree 5
  13. b_6_10, an element of degree 6
  14. b_6_11, an element of degree 6
  15. b_7_12, an element of degree 7
  16. b_7_14, an element of degree 7
  17. b_8_17, an element of degree 8
  18. c_8_18, a Duflot regular element of degree 8
  19. b_9_22, an element of degree 9

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Ring relations

There are 134 minimal relations of maximal degree 18:

  1. a_1_02
  2. a_1_0·b_1_1
  3. a_2_2·a_1_0
  4. a_2_2·b_1_1
  5. b_2_1·b_1_1
  6. a_2_2·b_2_1 + a_2_22
  7. a_1_0·b_3_2
  8. a_1_0·b_3_3 + a_2_22
  9. b_1_1·b_3_3 + a_2_22
  10. a_1_0·b_3_4
  11. a_2_2·b_3_2
  12. b_2_1·b_3_2
  13. a_2_2·b_3_3
  14. a_2_2·b_3_4
  15. b_2_1·b_3_4 + b_2_1·b_3_3
  16. b_4_4·a_1_0
  17. b_1_12·b_3_2 + b_4_4·b_1_1
  18. b_4_6·a_1_0
  19. b_3_2·b_3_3
  20. a_2_2·b_4_4
  21. b_3_3·b_3_4 + b_3_32 + a_2_2·b_4_6
  22. b_3_32 + b_2_1·b_4_6 + b_2_1·b_4_4
  23. b_3_22 + b_4_6·b_1_12 + b_4_4·b_1_12
  24. a_1_0·b_5_6
  25. b_1_1·b_5_6
  26. a_1_0·b_5_7
  27. b_3_42 + b_3_3·b_3_4 + b_1_1·b_5_7
  28. a_1_0·b_5_8
  29. b_3_2·b_3_4 + b_1_1·b_5_8 + b_4_4·b_1_12
  30. b_4_6·b_1_13 + b_4_4·b_3_2 + b_4_4·b_1_13
  31. a_2_2·b_5_6
  32. a_2_2·b_5_7
  33. b_2_1·b_5_7
  34. a_2_2·b_5_8
  35. b_4_4·b_3_3 + b_2_1·b_5_8 + b_2_1·b_5_6
  36. b_1_12·b_5_8 + b_4_4·b_3_4 + b_4_4·b_3_3 + b_4_4·b_1_13
  37. b_4_4·b_3_3 + b_2_1·b_5_6 + b_6_10·a_1_0
  38. b_1_12·b_5_7 + b_1_14·b_3_4 + b_6_10·b_1_1 + b_4_4·b_3_4 + b_4_4·b_3_3 + b_4_4·b_3_2
       + b_4_4·b_1_13
  39. b_4_4·b_3_3 + b_2_1·b_5_6 + b_6_11·a_1_0
  40. b_1_12·b_5_7 + b_6_11·b_1_1 + b_4_6·b_3_2 + b_4_4·b_1_13
  41. b_4_4·b_1_1·b_3_2 + b_4_42 + b_2_12·b_4_6 + b_2_12·b_4_4
  42. b_3_2·b_5_6
  43. b_3_4·b_5_6 + b_4_6·b_1_1·b_3_2 + b_4_4·b_1_1·b_3_2 + b_4_4·b_4_6 + b_4_42
  44. b_3_3·b_5_7 + b_3_3·b_5_6 + b_4_6·b_1_1·b_3_2 + b_4_4·b_1_1·b_3_2 + b_4_4·b_4_6 + b_4_42
  45. b_3_2·b_5_8 + b_4_6·b_1_1·b_3_4 + b_4_4·b_1_1·b_3_4 + b_4_4·b_1_1·b_3_2
  46. b_3_3·b_5_8 + b_3_3·b_5_6 + b_4_6·b_1_1·b_3_2 + b_4_4·b_1_1·b_3_2 + b_4_4·b_4_6 + b_4_42
  47. b_3_4·b_5_8 + b_3_2·b_5_7 + b_4_4·b_1_1·b_3_4
  48. a_2_2·b_6_10
  49. b_3_3·b_5_6 + b_4_6·b_1_1·b_3_2 + b_4_4·b_1_1·b_3_2 + b_4_4·b_4_6 + b_4_42
       + a_2_2·b_6_11
  50. b_3_3·b_5_6 + b_2_1·b_6_11 + b_2_1·b_6_10 + b_2_12·b_4_4
  51. a_1_0·b_7_12
  52. b_3_2·b_5_7 + b_1_1·b_7_12 + b_6_11·b_1_12 + b_6_10·b_1_12 + b_4_4·b_1_1·b_3_2
  53. a_1_0·b_7_14
  54. b_3_4·b_5_7 + b_1_1·b_7_14 + b_6_11·b_1_12
  55. b_4_6·b_1_12·b_3_4 + b_4_4·b_5_8 + b_4_4·b_1_12·b_3_4 + b_4_42·b_1_1
  56. b_4_4·b_5_6 + b_2_1·b_4_6·b_3_3 + b_2_12·b_5_6 + b_2_1·b_6_10·a_1_0
  57. b_6_10·b_3_2 + b_4_6·b_1_12·b_3_4 + b_4_4·b_5_7 + b_4_4·b_4_6·b_1_1
  58. b_6_11·b_3_2 + b_4_62·b_1_1 + b_4_4·b_5_7 + b_4_4·b_4_6·b_1_1 + b_4_42·b_1_1
  59. b_6_11·b_3_3 + b_6_10·b_3_3 + b_4_6·b_5_6 + b_2_1·b_4_6·b_3_3
  60. b_6_11·b_3_4 + b_6_11·b_1_13 + b_6_10·b_3_4 + b_4_6·b_5_8 + b_4_6·b_5_6
       + b_4_6·b_1_12·b_3_4 + b_4_4·b_5_7 + b_4_4·b_1_12·b_3_4 + b_4_4·b_1_15
       + b_2_1·b_4_6·b_3_3
  61. a_2_2·b_7_12
  62. b_2_1·b_7_12 + b_2_12·b_5_6 + b_2_13·b_3_3
  63. b_1_12·b_7_12 + b_6_11·b_1_13 + b_6_10·b_1_13 + b_4_4·b_5_7 + b_4_42·b_1_1
  64. a_2_2·b_7_14
  65. b_6_10·b_3_3 + b_2_1·b_7_14 + b_2_1·b_4_6·b_3_3
  66. b_1_12·b_7_14 + b_6_10·b_3_4 + b_6_10·b_3_3 + b_4_6·b_1_12·b_3_4 + b_4_4·b_5_7
       + b_4_4·b_1_15 + b_4_4·b_4_6·b_1_1
  67. b_8_17·a_1_0
  68. b_8_17·b_1_1 + b_6_11·b_1_13 + b_4_62·b_1_1 + b_4_4·b_5_7 + b_4_4·b_1_12·b_3_4
  69. b_5_62 + b_2_1·b_4_62 + b_2_13·b_4_6 + b_2_13·b_4_4
  70. b_5_6·b_5_7 + a_2_2·b_4_62
  71. b_5_82 + b_4_6·b_1_1·b_5_7 + b_4_4·b_1_1·b_5_7 + b_4_42·b_1_12 + a_2_2·b_4_62
  72. b_5_6·b_5_8 + a_2_2·b_4_62
  73. b_4_62·b_1_12 + b_4_4·b_1_1·b_5_8 + b_4_4·b_1_13·b_3_4 + b_4_4·b_6_11 + b_4_4·b_6_10
       + b_2_1·b_4_62 + a_2_2·b_4_62
  74. b_3_2·b_7_12 + b_4_6·b_1_1·b_5_7 + b_4_62·b_1_12 + b_4_4·b_1_1·b_5_8
       + b_4_4·b_1_1·b_5_7 + b_4_4·b_1_13·b_3_4 + b_4_4·b_4_6·b_1_12 + b_4_42·b_1_12
  75. b_3_3·b_7_12 + b_2_12·b_6_11 + b_2_12·b_6_10 + b_2_13·b_4_6 + a_2_2·b_4_62
  76. b_5_7·b_5_8 + b_3_4·b_7_12 + b_6_11·b_1_14 + b_4_6·b_1_1·b_5_8 + b_4_4·b_1_16
       + b_2_12·b_6_11 + b_2_12·b_6_10 + b_2_13·b_4_6 + a_2_2·b_4_62
  77. b_5_7·b_5_8 + b_3_2·b_7_14 + b_4_62·b_1_12 + b_4_4·b_4_6·b_1_12 + b_4_42·b_1_12
       + a_2_2·b_4_62
  78. b_3_3·b_7_14 + b_4_6·b_1_1·b_5_8 + b_4_6·b_1_1·b_5_7 + b_4_6·b_6_10 + b_4_62·b_1_12
       + b_4_4·b_1_1·b_5_7 + b_4_4·b_6_10 + b_2_1·b_4_62 + b_2_12·b_6_11 + b_2_12·b_6_10
       + b_2_13·b_4_6
  79. b_5_72 + b_3_4·b_7_14 + b_6_11·b_1_14 + b_6_10·b_1_1·b_3_4 + b_4_6·b_1_1·b_5_7
       + b_4_6·b_6_10 + b_4_62·b_1_12 + b_4_4·b_1_1·b_5_8 + b_4_4·b_1_16 + b_4_4·b_6_10
       + b_4_42·b_1_12 + b_2_1·b_4_62 + b_2_12·b_6_11 + b_2_12·b_6_10 + b_2_13·b_4_6
  80. b_5_72 + b_6_11·b_1_14 + b_6_10·b_1_14 + b_4_6·b_1_1·b_5_7 + b_4_4·b_1_1·b_5_7
       + b_4_4·b_1_13·b_3_4 + a_2_2·b_4_62 + c_8_18·b_1_12
  81. a_2_2·b_8_17 + a_2_2·b_4_62
  82. b_4_4·b_1_1·b_5_8 + b_4_4·b_1_1·b_5_7 + b_4_4·b_1_13·b_3_4 + b_4_4·b_6_10
       + b_4_4·b_4_6·b_1_12 + b_4_42·b_1_12 + b_2_1·b_8_17 + b_2_1·b_4_62
       + b_2_12·b_6_11 + b_2_12·b_6_10
  83. a_1_0·b_9_22
  84. b_5_7·b_5_8 + b_1_1·b_9_22 + b_6_10·b_1_14 + b_4_6·b_1_1·b_5_8 + b_4_4·b_1_1·b_5_7
       + b_4_4·b_1_13·b_3_4 + b_4_42·b_1_12 + a_2_2·b_4_62
  85. b_6_11·b_5_8 + b_6_10·b_5_8 + b_4_6·b_6_10·b_1_1 + b_4_62·b_3_4 + b_4_62·b_3_3
       + b_4_4·b_4_6·b_3_4 + b_4_42·b_3_4 + b_4_42·b_1_13 + b_2_1·b_4_6·b_5_6
       + b_2_12·b_4_6·b_3_3 + b_2_13·b_5_6 + b_2_12·b_6_10·a_1_0
  86. b_6_11·b_5_6 + b_6_10·b_5_6 + b_4_62·b_3_3
  87. b_4_6·b_6_10·b_1_1 + b_4_4·b_7_12 + b_4_4·b_6_11·b_1_1 + b_4_4·b_4_6·b_3_4
       + b_4_4·b_4_6·b_3_2 + b_4_42·b_3_2 + b_2_1·b_4_6·b_5_6 + b_2_12·b_4_6·b_3_3
  88. b_6_10·b_5_8 + b_6_10·b_5_6 + b_4_6·b_6_10·b_1_1 + b_4_4·b_7_14 + b_4_42·b_1_13
       + b_2_1·b_4_6·b_5_6
  89. b_6_11·b_5_7 + b_6_11·b_1_15 + b_6_10·b_1_15 + b_4_6·b_7_12 + b_4_6·b_6_10·b_1_1
       + b_4_62·b_3_2 + b_4_4·b_6_11·b_1_1 + b_4_4·b_6_10·b_1_1 + b_4_42·b_3_4
       + b_4_42·b_1_13 + b_2_1·b_4_6·b_5_6 + b_2_13·b_5_6 + b_2_12·b_6_10·a_1_0
       + c_8_18·b_1_13
  90. b_6_11·b_5_7 + b_6_11·b_1_15 + b_6_10·b_5_8 + b_6_10·b_5_7 + b_6_10·b_1_12·b_3_4
       + b_4_6·b_7_12 + b_4_62·b_3_2 + b_4_4·b_1_17 + b_4_4·b_6_10·b_1_1 + b_4_42·b_3_2
       + b_4_42·b_1_13 + b_2_1·b_4_6·b_5_6 + b_2_12·b_4_6·b_3_3 + b_2_1·c_8_18·a_1_0
  91. b_8_17·b_3_2 + b_4_6·b_6_10·b_1_1 + b_4_62·b_3_2 + b_4_4·b_6_11·b_1_1
       + b_4_4·b_6_10·b_1_1 + b_4_4·b_4_6·b_3_4 + b_4_4·b_4_6·b_3_2 + b_4_42·b_3_4
       + b_2_1·b_4_6·b_5_6 + b_2_12·b_4_6·b_3_3 + b_2_13·b_5_6 + b_2_12·b_6_10·a_1_0
  92. b_8_17·b_3_3 + b_6_11·b_5_7 + b_6_11·b_1_15 + b_6_10·b_5_8 + b_6_10·b_5_7 + b_6_10·b_5_6
       + b_6_10·b_1_12·b_3_4 + b_4_6·b_7_12 + b_4_62·b_3_3 + b_4_62·b_3_2 + b_4_4·b_1_17
       + b_4_4·b_6_10·b_1_1 + b_4_42·b_3_2 + b_4_42·b_1_13
  93. b_8_17·b_3_4 + b_6_11·b_1_15 + b_6_10·b_5_8 + b_6_10·b_5_6 + b_6_10·b_1_12·b_3_4
       + b_4_6·b_6_10·b_1_1 + b_4_62·b_3_4 + b_4_4·b_1_17 + b_4_4·b_6_11·b_1_1
       + b_4_4·b_4_6·b_3_4 + b_4_42·b_3_4 + b_4_42·b_3_2 + b_2_13·b_5_6
       + b_2_12·b_6_10·a_1_0
  94. a_2_2·b_9_22
  95. b_6_10·b_5_6 + b_2_1·b_9_22 + b_2_1·b_4_6·b_5_6 + b_2_14·b_3_3
  96. b_1_12·b_9_22 + b_6_11·b_5_7 + b_6_11·b_1_15 + b_6_10·b_5_7 + b_6_10·b_1_12·b_3_4
       + b_6_10·b_1_15 + b_4_6·b_7_12 + b_4_6·b_6_10·b_1_1 + b_4_62·b_3_2 + b_4_4·b_1_17
       + b_4_4·b_4_6·b_3_4 + b_4_4·b_4_6·b_3_2 + b_4_42·b_3_4 + b_4_42·b_3_2 + b_2_13·b_5_6
       + b_2_12·b_6_10·a_1_0
  97. b_5_6·b_7_12 + b_2_12·b_4_62 + b_2_13·b_6_11 + b_2_13·b_6_10 + b_2_14·b_4_6
       + a_2_2·b_4_6·b_6_11
  98. b_5_8·b_7_14 + b_5_8·b_7_12 + b_5_7·b_7_12 + b_6_11·b_1_16 + b_6_10·b_1_13·b_3_4
       + b_4_6·b_1_1·b_7_14 + b_4_6·b_1_1·b_7_12 + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18
       + b_4_4·b_4_6·b_1_1·b_3_4 + b_4_42·b_1_1·b_3_4 + b_4_42·b_1_14 + b_4_42·b_4_6
       + b_2_12·b_4_62 + b_2_13·b_6_11 + b_2_13·b_6_10 + b_2_14·b_4_6 + a_2_2·b_4_6·b_6_11
  99. b_5_8·b_7_14 + b_5_7·b_7_12 + b_6_11·b_1_16 + b_6_10·b_1_13·b_3_4
       + b_4_6·b_1_1·b_7_12 + b_4_62·b_1_1·b_3_4 + b_4_4·b_1_1·b_7_14 + b_4_4·b_1_18
       + b_4_4·b_6_11·b_1_12 + b_4_4·b_4_62 + b_4_42·b_1_1·b_3_4 + b_4_42·b_4_6 + b_4_43
       + b_2_1·b_4_6·b_6_11 + b_2_1·b_4_6·b_6_10 + b_2_14·b_4_6 + b_2_14·b_4_4
       + a_2_2·b_4_6·b_6_11
  100. b_5_8·b_7_14 + b_5_7·b_7_12 + b_5_6·b_7_14 + b_6_112 + b_6_10·b_1_16 + b_6_10·b_6_11
       + b_6_102 + b_4_63 + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18 + b_4_4·b_6_10·b_1_12
       + b_4_4·b_4_6·b_1_1·b_3_4 + b_4_42·b_4_6 + c_8_18·b_1_14 + b_2_12·c_8_18
  101. b_6_11·b_1_16 + b_6_112 + b_6_102 + b_4_63 + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18
       + b_4_4·b_6_11·b_1_12 + b_4_4·b_6_10·b_1_12 + b_4_4·b_4_62 + b_4_42·b_1_14
       + b_4_42·b_4_6 + b_4_43 + b_2_14·b_4_6 + b_2_14·b_4_4 + a_2_2·b_4_6·b_6_11
       + a_2_22·c_8_18
  102. b_5_8·b_7_14 + b_4_6·b_1_1·b_7_12 + b_4_62·b_1_1·b_3_4 + b_4_4·b_1_1·b_7_12
       + b_4_4·b_6_10·b_1_12 + b_4_4·b_4_62 + b_4_42·b_4_6 + b_2_1·b_4_6·b_6_11
       + b_2_1·b_4_6·b_6_10 + b_2_13·b_6_11 + b_2_13·b_6_10 + b_2_14·b_4_6
       + c_8_18·b_1_1·b_3_2
  103. b_5_8·b_7_12 + b_5_7·b_7_14 + b_6_10·b_1_16 + b_4_6·b_1_1·b_7_12 + b_4_62·b_1_1·b_3_4
       + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18 + b_4_4·b_4_6·b_1_1·b_3_4 + b_4_4·b_4_62
       + b_4_42·b_1_14 + b_4_43 + b_2_1·b_4_6·b_6_11 + b_2_1·b_4_6·b_6_10
       + b_2_12·b_4_62 + b_2_13·b_6_11 + b_2_13·b_6_10 + b_2_14·b_4_4 + a_2_2·b_4_6·b_6_11
       + c_8_18·b_1_1·b_3_4 + c_8_18·b_1_14
  104. b_5_8·b_7_14 + b_5_7·b_7_12 + b_5_6·b_7_14 + b_6_11·b_1_16 + b_6_10·b_6_11 + b_6_102
       + b_4_4·b_1_18 + b_4_4·b_6_10·b_1_12 + b_4_4·b_4_6·b_1_1·b_3_4 + b_4_4·b_4_62
       + b_4_42·b_1_1·b_3_4 + b_4_42·b_1_14 + b_2_12·b_8_17 + b_2_14·b_4_6
       + a_2_2·b_4_6·b_6_11
  105. b_5_8·b_7_14 + b_5_7·b_7_12 + b_6_11·b_1_16 + b_6_10·b_6_11 + b_6_102
       + b_4_6·b_1_1·b_7_12 + b_4_6·b_8_17 + b_4_63 + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18
       + b_4_4·b_6_11·b_1_12 + b_4_4·b_6_10·b_1_12 + b_4_4·b_4_6·b_1_1·b_3_4
       + b_4_4·b_4_62 + b_4_42·b_1_1·b_3_4 + b_4_42·b_1_14 + b_4_43 + b_2_1·b_4_6·b_6_10
       + b_2_12·b_4_62 + b_2_13·b_6_11 + b_2_13·b_6_10 + b_2_14·b_4_4 + a_2_2·b_4_6·b_6_11
  106. b_5_8·b_7_14 + b_5_7·b_7_12 + b_5_6·b_7_14 + b_6_11·b_1_16 + b_6_10·b_6_11 + b_6_102
       + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18 + b_4_4·b_8_17 + b_4_4·b_4_6·b_1_1·b_3_4
       + b_4_42·b_1_14 + b_4_43 + b_2_1·b_4_6·b_6_10 + b_2_14·b_4_6 + b_2_14·b_4_4
       + a_2_2·b_4_6·b_6_11
  107. b_5_8·b_7_12 + b_3_2·b_9_22 + b_4_42·b_1_1·b_3_4 + b_4_42·b_1_14
       + a_2_2·b_4_6·b_6_11
  108. b_5_6·b_7_14 + b_3_3·b_9_22 + b_6_11·b_1_16 + b_6_112 + b_6_102 + b_4_63
       + b_4_4·b_1_1·b_7_12 + b_4_4·b_1_18 + b_4_4·b_6_11·b_1_12 + b_4_4·b_6_10·b_1_12
       + b_4_4·b_4_62 + b_4_42·b_1_14 + b_4_42·b_4_6 + b_4_43
  109. b_5_8·b_7_14 + b_5_6·b_7_14 + b_3_4·b_9_22 + b_6_10·b_1_13·b_3_4 + b_4_6·b_1_1·b_7_12
       + b_4_62·b_1_1·b_3_4 + b_4_4·b_6_11·b_1_12 + b_4_4·b_6_10·b_1_12
       + b_4_4·b_4_6·b_1_1·b_3_4 + b_4_4·b_4_62 + b_4_42·b_1_14 + b_4_43
       + b_2_1·b_4_6·b_6_11 + b_2_1·b_4_6·b_6_10 + b_2_12·b_4_62 + b_2_13·b_6_11
       + b_2_13·b_6_10 + b_2_14·b_4_6 + a_2_2·b_4_6·b_6_11
  110. b_6_11·b_7_12 + b_6_112·b_1_1 + b_6_10·b_7_12 + b_6_102·b_1_1 + b_4_6·b_6_10·b_3_4
       + b_4_62·b_5_7 + b_4_4·b_6_11·b_1_13 + b_4_4·b_4_6·b_5_8 + b_4_4·b_4_6·b_5_7
       + b_4_4·b_4_62·b_1_1 + b_4_42·b_1_15 + b_4_43·b_1_1 + b_2_1·b_4_6·b_7_14
       + b_2_12·b_4_6·b_5_6 + b_2_13·b_4_6·b_3_3
  111. b_6_11·b_7_12 + b_6_112·b_1_1 + b_6_10·b_7_14 + b_6_10·b_7_12 + b_6_10·b_6_11·b_1_1
       + b_4_6·b_6_10·b_3_4 + b_4_62·b_5_7 + b_4_4·b_6_11·b_1_13 + b_4_4·b_6_10·b_3_4
       + b_4_4·b_6_10·b_1_13 + b_4_4·b_4_6·b_5_8 + b_4_4·b_4_62·b_1_1 + b_4_42·b_5_7
       + b_4_42·b_1_15 + b_2_12·b_4_6·b_5_6 + b_2_13·b_4_6·b_3_3 + c_8_18·b_1_12·b_3_4
       + b_4_4·c_8_18·b_1_1 + b_2_1·c_8_18·b_3_3
  112. b_8_17·b_5_8 + b_6_11·b_7_12 + b_6_112·b_1_1 + b_6_10·b_7_12 + b_6_102·b_1_1
       + b_4_62·b_5_8 + b_4_62·b_5_7 + b_4_4·b_6_11·b_1_13 + b_4_4·b_4_6·b_5_8
       + b_4_4·b_4_62·b_1_1 + b_4_42·b_5_8 + b_4_42·b_5_7 + b_4_42·b_1_12·b_3_4
       + b_4_42·b_4_6·b_1_1 + b_2_1·b_4_62·b_3_3 + b_2_12·b_4_6·b_5_6 + b_2_13·b_4_6·b_3_3
  113. b_8_17·b_5_6 + b_6_11·b_7_12 + b_6_112·b_1_1 + b_6_10·b_7_14 + b_6_102·b_1_1
       + b_4_62·b_5_7 + b_4_62·b_5_6 + b_4_4·b_6_11·b_1_13 + b_4_4·b_6_10·b_3_4
       + b_4_4·b_4_6·b_5_7 + b_4_4·b_4_62·b_1_1 + b_4_42·b_1_12·b_3_4 + b_4_42·b_4_6·b_1_1
       + b_2_1·b_4_62·b_3_3 + b_2_12·b_4_6·b_5_6 + b_2_13·b_7_14 + c_8_18·b_1_12·b_3_4
       + b_2_1·c_8_18·b_3_3 + b_2_12·c_8_18·a_1_0
  114. b_8_17·b_5_7 + b_6_11·b_7_12 + b_6_10·b_6_11·b_1_1 + b_4_63·b_1_1 + b_4_4·b_6_10·b_3_4
       + b_4_42·b_5_8 + b_4_42·b_5_7 + b_4_42·b_1_12·b_3_4 + b_4_42·b_1_15
       + b_4_42·b_4_6·b_1_1 + b_2_1·b_4_62·b_3_3 + b_2_12·b_4_6·b_5_6 + b_2_13·b_7_14
       + b_2_12·c_8_18·a_1_0
  115. b_6_10·b_7_14 + b_6_10·b_7_12 + b_4_6·b_6_10·b_3_4 + b_4_4·b_6_10·b_3_4
       + b_4_4·b_4_6·b_5_8 + b_4_42·b_1_12·b_3_4 + b_4_42·b_1_15 + b_4_42·b_4_6·b_1_1
       + b_4_43·b_1_1 + b_2_1·b_4_62·b_3_3 + b_2_12·b_9_22 + b_2_12·b_4_6·b_5_6
       + b_2_13·b_7_14 + b_2_13·b_4_6·b_3_3 + b_2_15·b_3_3 + c_8_18·b_1_12·b_3_4
       + b_2_1·c_8_18·b_3_3
  116. b_6_11·b_7_14 + b_6_11·b_7_12 + b_6_112·b_1_1 + b_6_10·b_7_14 + b_4_6·b_9_22
       + b_4_6·b_6_10·b_3_4 + b_4_62·b_5_8 + b_4_62·b_5_7 + b_4_63·b_1_1 + b_4_4·b_6_10·b_3_4
       + b_4_4·b_6_10·b_1_13 + b_4_4·b_4_6·b_5_8 + b_4_42·b_5_7 + b_4_42·b_1_15
       + b_4_43·b_1_1 + b_2_12·b_4_6·b_5_6 + b_2_13·b_7_14 + b_2_13·b_4_6·b_3_3
       + b_2_12·c_8_18·a_1_0
  117. b_4_6·b_6_10·b_3_4 + b_4_4·b_9_22 + b_4_4·b_6_10·b_3_4 + b_4_4·b_6_10·b_1_13
       + b_4_4·b_4_6·b_5_7 + b_4_42·b_1_12·b_3_4 + b_4_42·b_4_6·b_1_1 + b_4_43·b_1_1
       + b_2_1·b_4_62·b_3_3 + b_2_12·b_4_6·b_5_6 + b_2_14·b_5_6 + b_2_13·b_6_10·a_1_0
  118. b_7_122 + b_6_112·b_1_12 + b_6_102·b_1_12 + b_4_62·b_1_1·b_5_7
       + b_4_42·b_1_13·b_3_4 + b_4_42·b_6_11 + b_4_43·b_1_12 + b_2_12·b_4_6·b_6_11
       + b_2_13·b_8_17 + b_2_13·b_4_62 + b_2_14·b_6_11 + b_2_14·b_6_10 + a_2_2·b_4_63
       + b_4_6·c_8_18·b_1_12 + b_4_4·c_8_18·b_1_12
  119. b_7_122 + b_6_11·b_8_17 + b_6_102·b_1_12 + b_4_62·b_1_1·b_5_8
       + b_4_62·b_1_1·b_5_7 + b_4_62·b_6_11 + b_4_62·b_6_10 + b_4_4·b_6_10·b_1_1·b_3_4
       + b_4_4·b_6_10·b_1_14 + b_4_4·b_4_6·b_1_1·b_5_7 + b_4_4·b_4_6·b_6_11
       + b_4_42·b_1_1·b_5_7 + b_4_42·b_1_13·b_3_4 + b_4_42·b_1_16 + b_4_42·b_6_11
       + b_4_43·b_1_12 + b_2_12·b_4_6·b_6_11 + b_2_13·b_4_62 + b_4_6·c_8_18·b_1_12
       + b_2_1·b_4_4·c_8_18
  120. b_7_12·b_7_14 + b_6_10·b_8_17 + b_4_62·b_1_1·b_5_7 + b_4_62·b_6_10
       + b_4_4·b_6_11·b_1_14 + b_4_4·b_6_10·b_1_14 + b_4_4·b_4_6·b_1_1·b_5_7
       + b_4_4·b_4_6·b_6_11 + b_4_4·b_4_6·b_6_10 + b_4_42·b_1_1·b_5_7 + b_4_42·b_1_16
       + b_4_42·b_6_10 + b_4_42·b_4_6·b_1_12 + b_4_43·b_1_12 + b_2_1·b_4_63
       + b_2_12·b_4_6·b_6_10 + c_8_18·b_1_1·b_5_8 + b_2_1·b_4_4·c_8_18
  121. b_7_142 + b_7_122 + b_6_112·b_1_12 + b_6_10·b_6_11·b_1_12 + b_6_102·b_1_12
       + b_4_4·b_6_10·b_1_1·b_3_4 + b_4_4·b_6_10·b_1_14 + b_4_4·b_4_6·b_6_11
       + b_4_4·b_4_6·b_6_10 + b_4_42·b_1_16 + b_4_42·b_6_10 + b_4_42·b_4_6·b_1_12
       + b_4_43·b_1_12 + b_2_1·b_4_6·b_8_17 + b_2_12·b_4_6·b_6_11 + b_2_12·b_4_6·b_6_10
       + b_2_13·b_4_62 + a_2_2·b_4_63 + c_8_18·b_1_1·b_5_7 + b_2_1·b_4_6·c_8_18
       + b_2_1·b_4_4·c_8_18 + a_2_2·b_4_6·c_8_18
  122. b_7_142 + b_7_12·b_7_14 + b_7_122 + b_5_8·b_9_22 + b_6_112·b_1_12
       + b_6_102·b_1_12 + b_4_62·b_1_1·b_5_7 + b_4_4·b_6_11·b_1_14 + b_4_42·b_1_16
       + b_4_42·b_6_11 + b_4_42·b_4_6·b_1_12 + b_4_43·b_1_12 + b_2_13·b_4_62
       + a_2_2·b_4_63 + c_8_18·b_1_1·b_5_8 + c_8_18·b_1_1·b_5_7 + b_4_6·c_8_18·b_1_12
       + b_2_1·b_4_6·c_8_18 + b_2_1·b_4_4·c_8_18 + a_2_2·b_4_6·c_8_18
  123. b_7_12·b_7_14 + b_6_10·b_6_11·b_1_12 + b_4_62·b_1_1·b_5_7 + b_4_4·b_1_1·b_9_22
       + b_4_4·b_6_11·b_1_14 + b_4_4·b_6_10·b_1_14 + b_4_4·b_4_6·b_6_11 + b_4_42·b_6_11
       + b_4_42·b_6_10 + b_4_43·b_1_12 + b_2_1·b_4_63 + c_8_18·b_1_1·b_5_8
       + b_4_4·c_8_18·b_1_12
  124. b_5_6·b_9_22 + b_4_62·b_1_1·b_5_8 + b_4_62·b_1_1·b_5_7 + b_4_62·b_6_10
       + b_4_4·b_4_6·b_6_11 + b_4_4·b_4_6·b_6_10 + b_4_42·b_1_1·b_5_7 + b_4_42·b_6_11
       + b_4_43·b_1_12 + b_2_12·b_4_6·b_6_11 + b_2_12·b_4_6·b_6_10 + b_2_15·b_4_6
       + b_2_15·b_4_4
  125. b_7_142 + b_7_12·b_7_14 + b_7_122 + b_5_7·b_9_22 + b_6_112·b_1_12
       + b_6_10·b_6_11·b_1_12 + b_6_102·b_1_12 + b_4_62·b_1_1·b_5_7
       + b_4_4·b_6_11·b_1_14 + b_4_4·b_4_6·b_1_1·b_5_7 + b_4_42·b_1_16 + b_4_42·b_6_11
       + b_4_43·b_1_12 + b_2_13·b_4_62 + a_2_2·b_4_63 + c_8_18·b_1_1·b_5_7
       + b_2_1·b_4_6·c_8_18 + b_2_1·b_4_4·c_8_18 + a_2_2·b_4_6·c_8_18
  126. b_8_17·b_7_14 + b_8_17·b_7_12 + b_6_112·b_1_13 + b_6_102·b_3_4 + b_4_62·b_7_14
       + b_4_62·b_7_12 + b_4_4·b_4_62·b_3_2 + b_4_42·b_7_12 + b_4_42·b_4_6·b_3_4
       + b_4_43·b_3_2 + b_4_43·b_1_13 + b_2_12·b_4_6·b_7_14 + b_2_12·b_4_62·b_3_3
       + b_2_13·b_4_6·b_5_6 + b_2_14·b_4_6·b_3_3 + b_4_4·c_8_18·b_3_4 + b_4_4·c_8_18·b_3_2
       + b_4_4·c_8_18·b_1_13 + b_2_12·c_8_18·b_3_3
  127. b_8_17·b_7_14 + b_6_102·b_1_13 + b_4_62·b_7_14 + b_4_4·b_6_11·b_1_15
       + b_4_4·b_4_6·b_7_12 + b_4_42·b_1_17 + b_4_42·b_4_6·b_3_4 + b_4_43·b_3_4
       + b_4_43·b_1_13 + b_2_12·b_4_62·b_3_3 + b_2_13·b_9_22 + b_2_13·b_4_6·b_5_6
       + b_2_14·b_4_6·b_3_3 + b_2_15·b_5_6 + b_2_16·b_3_3 + b_2_14·b_6_10·a_1_0
       + b_6_11·c_8_18·b_1_1 + b_6_10·c_8_18·b_1_1 + b_4_6·c_8_18·b_3_2 + b_4_4·c_8_18·b_3_2
       + b_2_1·c_8_18·b_5_6 + b_6_10·c_8_18·a_1_0 + b_2_13·c_8_18·a_1_0
  128. b_6_11·b_9_22 + b_6_102·b_3_4 + b_6_102·b_1_13 + b_4_62·b_7_14 + b_4_63·b_3_4
       + b_4_63·b_3_3 + b_4_63·b_3_2 + b_4_4·b_6_10·b_1_15 + b_4_4·b_4_6·b_7_14
       + b_4_4·b_4_6·b_7_12 + b_4_4·b_4_62·b_3_4 + b_4_4·b_4_62·b_3_2 + b_4_42·b_1_17
       + b_4_42·b_6_11·b_1_1 + b_4_43·b_3_4 + b_4_43·b_3_2 + b_2_1·b_4_62·b_5_6
       + b_2_12·b_4_6·b_7_14 + b_2_12·b_4_62·b_3_3 + b_2_14·b_7_14 + b_2_14·b_4_6·b_3_3
       + b_2_15·b_5_6 + b_2_14·b_6_10·a_1_0 + b_6_11·c_8_18·b_1_1 + b_6_10·c_8_18·b_1_1
       + b_4_6·c_8_18·b_3_2 + b_4_4·c_8_18·b_3_2 + b_2_1·c_8_18·b_5_6 + b_2_12·c_8_18·b_3_3
  129. b_6_10·b_9_22 + b_6_102·b_1_13 + b_4_4·b_6_10·b_1_12·b_3_4 + b_4_4·b_6_10·b_1_15
       + b_4_4·b_4_6·b_7_14 + b_4_4·b_4_62·b_3_4 + b_4_4·b_4_62·b_3_2 + b_4_42·b_7_14
       + b_4_42·b_7_12 + b_4_42·b_1_17 + b_4_42·b_6_10·b_1_1 + b_4_43·b_3_4
       + b_2_1·b_4_62·b_5_6 + b_2_12·b_4_62·b_3_3 + b_2_13·b_4_6·b_5_6 + b_2_14·b_7_14
       + b_2_15·b_5_6 + b_2_14·b_6_10·a_1_0 + b_4_4·c_8_18·b_3_4 + b_4_4·c_8_18·b_3_2
       + b_4_4·c_8_18·b_1_13 + b_6_10·c_8_18·a_1_0
  130. b_8_172 + b_6_112·b_1_14 + b_4_64 + b_4_4·b_4_6·b_8_17 + b_4_4·b_4_63
       + b_4_42·b_6_11·b_1_12 + b_4_42·b_6_10·b_1_12 + b_4_42·b_4_6·b_1_1·b_3_4
       + b_4_42·b_4_62 + b_4_43·b_1_1·b_3_4 + b_4_43·b_1_14 + b_4_44
       + b_2_1·b_4_62·b_6_10 + b_2_13·b_4_6·b_6_11 + b_2_14·b_8_17 + b_2_15·b_6_11
       + b_2_15·b_6_10 + b_2_16·b_4_6 + b_2_16·b_4_4 + b_4_42·c_8_18
  131. b_7_14·b_9_22 + b_6_102·b_1_1·b_3_4 + b_4_62·b_1_1·b_7_14 + b_4_63·b_1_1·b_3_4
       + b_4_4·b_6_102 + b_4_4·b_4_6·b_8_17 + b_4_4·b_4_62·b_1_1·b_3_4
       + b_4_42·b_1_1·b_7_14 + b_4_42·b_1_18 + b_4_42·b_6_10·b_1_12 + b_4_43·b_1_14
       + b_2_1·b_4_62·b_6_11 + b_2_1·b_4_62·b_6_10 + b_2_12·b_4_6·b_8_17 + b_2_12·b_4_63
       + b_2_13·b_4_6·b_6_10 + b_2_14·b_8_17 + b_2_14·b_4_62 + b_2_16·b_4_6
       + a_2_2·b_4_62·b_6_11 + c_8_18·b_1_1·b_7_12 + b_6_11·c_8_18·b_1_12
       + b_6_10·c_8_18·b_1_12 + b_4_4·c_8_18·b_1_1·b_3_4 + b_4_4·c_8_18·b_1_14
       + b_2_1·b_6_11·c_8_18 + b_2_1·b_6_10·c_8_18 + a_2_2·b_6_11·c_8_18
  132. b_7_12·b_9_22 + b_6_102·b_1_1·b_3_4 + b_4_62·b_1_1·b_7_14 + b_4_63·b_1_1·b_3_4
       + b_4_4·b_6_102 + b_4_4·b_4_63 + b_4_42·b_1_1·b_7_14 + b_4_42·b_6_11·b_1_12
       + b_4_42·b_6_10·b_1_12 + b_4_42·b_4_62 + b_4_43·b_4_6 + b_2_1·b_4_62·b_6_11
       + b_2_12·b_4_6·b_8_17 + b_2_13·b_4_6·b_6_11 + b_2_14·b_8_17 + b_2_15·b_6_11
       + b_2_15·b_6_10 + a_2_2·b_4_62·b_6_11 + b_6_11·c_8_18·b_1_12
       + b_6_10·c_8_18·b_1_12 + b_4_6·c_8_18·b_1_1·b_3_4 + b_4_4·c_8_18·b_1_14
       + b_4_4·b_4_6·c_8_18 + b_2_1·b_6_11·c_8_18 + b_2_1·b_6_10·c_8_18 + b_2_12·b_4_6·c_8_18
       + b_2_12·b_4_4·c_8_18 + a_2_2·b_6_11·c_8_18
  133. b_8_17·b_9_22 + b_6_102·b_1_12·b_3_4 + b_6_102·b_1_15 + b_4_62·b_9_22
       + b_4_4·b_4_6·b_9_22 + b_4_42·b_9_22 + b_4_42·b_6_11·b_1_13 + b_4_42·b_4_6·b_5_7
       + b_4_43·b_5_8 + b_4_43·b_5_7 + b_4_43·b_1_12·b_3_4 + b_4_43·b_1_15
       + b_4_43·b_4_6·b_1_1 + b_4_44·b_1_1 + b_2_1·b_4_62·b_7_14 + b_2_12·b_4_62·b_5_6
       + b_2_13·b_4_62·b_3_3 + b_2_14·b_9_22 + b_2_16·b_5_6 + b_2_17·b_3_3
       + b_2_15·b_6_10·a_1_0 + b_6_11·c_8_18·b_1_13 + b_6_10·c_8_18·b_1_13
       + b_4_4·c_8_18·b_5_8 + b_4_4·c_8_18·b_1_15 + b_4_4·b_4_6·c_8_18·b_1_1
       + b_4_42·c_8_18·b_1_1 + b_2_1·b_4_6·c_8_18·b_3_3 + b_2_12·c_8_18·b_5_6
       + b_2_1·b_6_10·c_8_18·a_1_0 + b_2_14·c_8_18·a_1_0
  134. b_9_222 + b_6_103 + b_4_4·b_6_10·b_6_11·b_1_12 + b_4_4·b_4_62·b_1_1·b_5_7
       + b_4_42·b_1_110 + b_4_42·b_6_11·b_1_14 + b_4_42·b_6_10·b_1_14
       + b_4_42·b_4_6·b_6_11 + b_4_43·b_6_11 + b_4_43·b_6_10 + b_4_43·b_4_6·b_1_12
       + b_2_1·b_4_62·b_8_17 + b_2_1·b_4_64 + b_2_17·b_4_6 + b_2_17·b_4_4
       + b_6_10·c_8_18·b_1_14 + b_4_6·c_8_18·b_1_1·b_5_7 + b_4_4·c_8_18·b_1_16
       + b_4_4·b_6_11·c_8_18 + b_4_4·b_4_6·c_8_18·b_1_12 + b_2_1·b_8_17·c_8_18
       + b_2_1·b_4_62·c_8_18 + b_2_12·b_6_11·c_8_18 + b_2_13·b_4_6·c_8_18

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Data used for Benson′s test

  • Benson′s completion test succeeded in degree 18.
  • The completion test was perfect: It applied in the last degree in which a generator or relation was found.
  • The following is a filter regular homogeneous system of parameters:
    1. c_8_18, a Duflot regular element of degree 8
    2. b_1_14 + b_4_6 + b_4_4 + b_2_12, an element of degree 4
    3. b_3_3 + b_3_2, an element of degree 3
  • The Raw Filter Degree Type of that HSOP is [-1, 4, 9, 12].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 1

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. a_2_2 → 0, an element of degree 2
  4. b_2_1 → 0, an element of degree 2
  5. b_3_2 → 0, an element of degree 3
  6. b_3_3 → 0, an element of degree 3
  7. b_3_4 → 0, an element of degree 3
  8. b_4_4 → 0, an element of degree 4
  9. b_4_6 → 0, an element of degree 4
  10. b_5_6 → 0, an element of degree 5
  11. b_5_7 → 0, an element of degree 5
  12. b_5_8 → 0, an element of degree 5
  13. b_6_10 → 0, an element of degree 6
  14. b_6_11 → 0, an element of degree 6
  15. b_7_12 → 0, an element of degree 7
  16. b_7_14 → 0, an element of degree 7
  17. b_8_17 → 0, an element of degree 8
  18. c_8_18 → c_1_08, an element of degree 8
  19. b_9_22 → 0, an element of degree 9

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → c_1_1, an element of degree 1
  3. a_2_2 → 0, an element of degree 2
  4. b_2_1 → 0, an element of degree 2
  5. b_3_2 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  6. b_3_3 → 0, an element of degree 3
  7. b_3_4 → c_1_0·c_1_12 + c_1_02·c_1_1, an element of degree 3
  8. b_4_4 → c_1_12·c_1_22 + c_1_13·c_1_2, an element of degree 4
  9. b_4_6 → c_1_24 + c_1_13·c_1_2, an element of degree 4
  10. b_5_6 → 0, an element of degree 5
  11. b_5_7 → c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_5_8 → c_1_13·c_1_22 + c_1_14·c_1_2 + c_1_0·c_1_12·c_1_22 + c_1_0·c_1_13·c_1_2
       + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2, an element of degree 5
  13. b_6_10 → c_1_12·c_1_24 + c_1_15·c_1_2 + c_1_0·c_1_13·c_1_22 + c_1_0·c_1_14·c_1_2
       + c_1_0·c_1_15 + c_1_02·c_1_12·c_1_22 + c_1_02·c_1_13·c_1_2 + c_1_04·c_1_12, an element of degree 6
  14. b_6_11 → c_1_26 + c_1_1·c_1_25 + c_1_13·c_1_23 + c_1_15·c_1_2 + c_1_02·c_1_14
       + c_1_04·c_1_12, an element of degree 6
  15. b_7_12 → c_1_1·c_1_26 + c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_15·c_1_22
       + c_1_0·c_1_14·c_1_22 + c_1_0·c_1_15·c_1_2 + c_1_0·c_1_16 + c_1_02·c_1_15
       + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_2, an element of degree 7
  16. b_7_14 → c_1_1·c_1_26 + c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_16·c_1_2 + c_1_02·c_1_15
       + c_1_03·c_1_14 + c_1_05·c_1_12 + c_1_06·c_1_1, an element of degree 7
  17. b_8_17 → c_1_28 + c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_15·c_1_23 + c_1_16·c_1_22
       + c_1_17·c_1_2 + c_1_0·c_1_15·c_1_22 + c_1_0·c_1_16·c_1_2 + c_1_02·c_1_16
       + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_13·c_1_2 + c_1_04·c_1_14, an element of degree 8
  18. c_8_18 → c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_14·c_1_24 + c_1_15·c_1_23
       + c_1_0·c_1_17 + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22
       + c_1_02·c_1_16 + c_1_04·c_1_24 + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_14
       + c_1_08, an element of degree 8
  19. b_9_22 → c_1_13·c_1_26 + c_1_14·c_1_25 + c_1_16·c_1_23 + c_1_18·c_1_2
       + c_1_0·c_1_12·c_1_26 + c_1_0·c_1_13·c_1_25 + c_1_0·c_1_15·c_1_23
       + c_1_0·c_1_16·c_1_22 + c_1_0·c_1_18 + c_1_02·c_1_1·c_1_26
       + c_1_02·c_1_12·c_1_25 + c_1_02·c_1_14·c_1_23 + c_1_02·c_1_15·c_1_22
       + c_1_03·c_1_14·c_1_22 + c_1_03·c_1_15·c_1_2 + c_1_04·c_1_13·c_1_22
       + c_1_04·c_1_14·c_1_2 + c_1_04·c_1_15 + c_1_05·c_1_12·c_1_22
       + c_1_05·c_1_13·c_1_2 + c_1_06·c_1_1·c_1_22 + c_1_06·c_1_12·c_1_2, an element of degree 9

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_0 → 0, an element of degree 1
  2. b_1_1 → 0, an element of degree 1
  3. a_2_2 → 0, an element of degree 2
  4. b_2_1 → c_1_12, an element of degree 2
  5. b_3_2 → 0, an element of degree 3
  6. b_3_3 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  7. b_3_4 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_4_4 → c_1_12·c_1_22 + c_1_13·c_1_2, an element of degree 4
  9. b_4_6 → c_1_24 + c_1_13·c_1_2, an element of degree 4
  10. b_5_6 → c_1_1·c_1_24 + c_1_13·c_1_22, an element of degree 5
  11. b_5_7 → 0, an element of degree 5
  12. b_5_8 → 0, an element of degree 5
  13. b_6_10 → c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_0·c_1_13·c_1_22 + c_1_0·c_1_14·c_1_2
       + c_1_02·c_1_12·c_1_22 + c_1_02·c_1_13·c_1_2 + c_1_02·c_1_14
       + c_1_04·c_1_12, an element of degree 6
  14. b_6_11 → c_1_26 + c_1_1·c_1_25 + c_1_13·c_1_23 + c_1_15·c_1_2 + c_1_0·c_1_13·c_1_22
       + c_1_0·c_1_14·c_1_2 + c_1_02·c_1_12·c_1_22 + c_1_02·c_1_13·c_1_2
       + c_1_02·c_1_14 + c_1_04·c_1_12, an element of degree 6
  15. b_7_12 → c_1_13·c_1_24 + c_1_16·c_1_2, an element of degree 7
  16. b_7_14 → c_1_13·c_1_24 + c_1_15·c_1_22 + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_14·c_1_22
       + c_1_02·c_1_1·c_1_24 + c_1_02·c_1_14·c_1_2 + c_1_04·c_1_1·c_1_22
       + c_1_04·c_1_12·c_1_2, an element of degree 7
  17. b_8_17 → c_1_28 + c_1_17·c_1_2 + c_1_0·c_1_13·c_1_24 + c_1_0·c_1_15·c_1_22
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_15·c_1_2 + c_1_04·c_1_12·c_1_22
       + c_1_04·c_1_13·c_1_2, an element of degree 8
  18. c_8_18 → c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_15·c_1_23 + c_1_16·c_1_22
       + c_1_0·c_1_13·c_1_24 + c_1_0·c_1_15·c_1_22 + c_1_02·c_1_14·c_1_22
       + c_1_02·c_1_15·c_1_2 + c_1_04·c_1_24 + c_1_04·c_1_13·c_1_2 + c_1_04·c_1_14
       + c_1_08, an element of degree 8
  19. b_9_22 → c_1_13·c_1_26 + c_1_14·c_1_25 + c_1_15·c_1_24 + c_1_16·c_1_23
       + c_1_17·c_1_22 + c_1_18·c_1_2 + c_1_0·c_1_12·c_1_26 + c_1_0·c_1_13·c_1_25
       + c_1_0·c_1_14·c_1_24 + c_1_0·c_1_15·c_1_23 + c_1_02·c_1_1·c_1_26
       + c_1_02·c_1_12·c_1_25 + c_1_02·c_1_14·c_1_23 + c_1_02·c_1_15·c_1_22
       + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_13·c_1_22, an element of degree 9

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 128


Simon A. King David J. Green
Fakultät für Mathematik und Informatik Fakultät für Mathematik und Informatik
Friedrich-Schiller-Universität Jena Friedrich-Schiller-Universität Jena
Ernst-Abbe-Platz 2 Ernst-Abbe-Platz 2
D-07743 Jena D-07743 Jena
Germany Germany
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46184
Fax: +49 (0)3641 9-46162
Office: Zi. 3524, Ernst-Abbe-Platz 2
E-mail: david dot green at uni hyphen jena dot de
Tel: +49 3641 9-46166
Fax: +49 3641 9-46162
Office: Zi 3512, Ernst-Abbe-Platz 2

Last change: 25.08.2009