Cohomology of group number 73 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 16.
  • 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 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    ( − 1) · (t5  +  t3  +  1)
    (t  +  1) · (t  −  1)3 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-∞,-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 20 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_1, a nilpotent element of degree 2
  4. b_2_2, 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. a_4_4, a nilpotent element of degree 4
  9. b_4_6, an element of degree 4
  10. b_5_5, 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_5_9, an element of degree 5
  14. b_6_11, an element of degree 6
  15. b_6_12, an element of degree 6
  16. b_7_14, an element of degree 7
  17. b_7_15, an element of degree 7
  18. a_8_5, a nilpotent element of degree 8
  19. c_8_19, a Duflot regular element of degree 8
  20. b_9_23, 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 152 minimal relations of maximal degree 18:

  1. a_1_02
  2. a_1_0·b_1_1
  3. a_2_1·a_1_0
  4. a_2_1·b_1_1
  5. b_2_2·b_1_1
  6. a_2_12
  7. a_1_0·b_3_2
  8. a_1_0·b_3_3 + a_2_1·b_2_2
  9. b_1_1·b_3_3
  10. a_1_0·b_3_4
  11. b_2_2·b_3_2
  12. a_2_1·b_3_2
  13. b_2_22·a_1_0 + a_2_1·b_3_3
  14. b_2_2·b_3_4
  15. a_2_1·b_3_4
  16. a_4_4·a_1_0
  17. a_4_4·b_1_1
  18. b_4_6·a_1_0
  19. b_3_2·b_3_3
  20. a_2_1·a_4_4
  21. b_3_3·b_3_4 + b_3_32 + b_2_2·b_4_6 + b_2_23 + b_2_2·a_4_4
  22. b_3_3·b_3_4 + a_2_1·b_4_6
  23. b_3_22 + b_1_13·b_3_4 + b_4_6·b_1_12
  24. a_1_0·b_5_5
  25. b_3_22 + b_1_1·b_5_5 + b_1_13·b_3_4 + b_1_13·b_3_2
  26. a_1_0·b_5_7 + a_2_1·b_2_22
  27. b_3_42 + b_1_1·b_5_7 + b_1_13·b_3_2
  28. a_1_0·b_5_8 + b_2_2·a_4_4 + a_2_1·b_2_22
  29. b_3_42 + b_1_1·b_5_8
  30. a_1_0·b_5_9
  31. b_3_42 + b_3_2·b_3_4 + b_3_22 + b_1_1·b_5_9 + b_1_13·b_3_4 + b_1_13·b_3_2
  32. a_4_4·b_3_2
  33. a_4_4·b_3_4
  34. a_2_1·b_5_5
  35. b_2_2·b_5_7 + b_2_22·b_3_3
  36. a_2_1·b_5_7 + a_2_1·b_2_2·b_3_3
  37. a_4_4·b_3_3 + a_2_1·b_5_8 + a_2_1·b_2_2·b_3_3
  38. b_2_2·b_5_9 + b_2_2·b_5_5 + a_4_4·b_3_3
  39. a_2_1·b_5_9
  40. b_6_11·a_1_0 + a_4_4·b_3_3
  41. b_1_12·b_5_9 + b_1_14·b_3_4 + b_6_11·b_1_1
  42. b_6_12·a_1_0 + a_4_4·b_3_3 + a_2_1·b_2_2·b_3_3
  43. b_1_14·b_3_4 + b_1_14·b_3_2 + b_6_12·b_1_1 + b_4_6·b_3_2
  44. a_4_42
  45. b_3_3·b_5_7 + b_2_22·b_4_6 + b_2_24 + a_4_4·b_4_6 + b_2_22·a_4_4
  46. b_3_2·b_5_8 + b_3_2·b_5_7 + b_3_2·b_5_5 + b_4_6·b_1_1·b_3_2
  47. b_3_4·b_5_8 + b_3_4·b_5_7 + b_3_4·b_5_5 + b_4_6·b_1_1·b_3_4 + a_4_4·b_4_6
  48. b_3_2·b_5_9 + b_3_2·b_5_7 + b_1_13·b_5_7 + b_1_15·b_3_2 + b_4_6·b_1_1·b_3_4
       + b_4_6·b_1_1·b_3_2
  49. b_3_3·b_5_9 + b_3_3·b_5_5 + b_2_22·a_4_4
  50. b_3_4·b_5_9 + b_3_4·b_5_7 + b_3_2·b_5_7 + b_3_2·b_5_5 + b_4_6·b_1_1·b_3_4
       + b_4_6·b_1_1·b_3_2 + a_4_4·b_4_6
  51. b_3_3·b_5_8 + b_2_2·b_6_11 + b_2_22·b_4_6 + b_2_24 + a_4_4·b_4_6 + a_2_1·b_2_23
  52. b_2_22·a_4_4 + a_2_1·b_6_11
  53. b_3_4·b_5_5 + b_3_2·b_5_5 + b_1_13·b_5_7 + b_6_11·b_1_12 + b_4_6·b_1_1·b_3_4
       + b_4_6·b_1_1·b_3_2 + a_4_4·b_4_6
  54. b_3_3·b_5_8 + b_3_3·b_5_5 + b_2_2·b_6_12
  55. a_4_4·b_4_6 + b_2_22·a_4_4 + a_2_1·b_6_12 + a_2_1·b_2_23
  56. b_3_2·b_5_5 + b_1_15·b_3_2 + b_6_12·b_1_12 + b_4_6·b_1_14
  57. a_1_0·b_7_14 + a_2_1·b_2_23
  58. b_3_2·b_5_7 + b_3_2·b_5_5 + b_1_1·b_7_14 + b_1_13·b_5_7 + b_1_15·b_3_2
       + b_4_6·b_1_1·b_3_4
  59. a_1_0·b_7_15
  60. b_3_4·b_5_7 + b_3_4·b_5_5 + b_1_1·b_7_15 + b_4_6·b_1_14 + a_4_4·b_4_6
  61. a_4_4·b_5_5
  62. a_4_4·b_5_7 + a_2_1·b_2_2·b_5_8 + a_2_1·b_2_22·b_3_3
  63. a_4_4·b_5_8 + a_4_4·b_5_7
  64. a_4_4·b_5_9
  65. b_6_11·b_3_3 + b_4_6·b_5_8 + b_4_6·b_5_7 + b_4_6·b_1_12·b_3_2 + b_2_22·b_5_8
       + b_2_23·b_3_3 + a_4_4·b_5_7 + a_2_1·b_2_22·b_3_3
  66. b_1_14·b_5_7 + b_6_12·b_3_2 + b_6_11·b_1_13 + b_4_6·b_1_12·b_3_4 + b_4_62·b_1_1
  67. b_6_12·b_3_3 + b_4_6·b_5_8 + b_4_6·b_5_7 + b_4_6·b_5_5 + b_4_62·b_1_1 + b_2_2·b_4_6·b_3_3
       + b_2_22·b_5_8 + b_2_22·b_5_5 + a_4_4·b_5_7
  68. b_6_12·b_3_4 + b_6_12·b_1_13 + b_6_11·b_1_13 + b_4_6·b_5_9 + b_4_6·b_5_7 + b_4_6·b_5_5
       + b_4_6·b_1_15 + b_2_2·b_4_6·b_3_3
  69. b_2_2·b_7_14 + b_2_2·b_4_6·b_3_3 + b_2_22·b_5_5 + b_2_23·b_3_3 + a_4_4·b_5_7
       + a_2_1·b_2_22·b_3_3
  70. a_2_1·b_7_14 + a_2_1·b_2_22·b_3_3
  71. b_1_12·b_7_14 + b_1_14·b_5_7 + b_6_11·b_3_2 + b_6_11·b_1_13
  72. b_4_6·b_5_8 + b_4_6·b_5_7 + b_4_6·b_1_12·b_3_2 + b_2_2·b_7_15 + b_2_2·b_4_6·b_3_3
       + b_2_22·b_5_5 + a_4_4·b_5_7
  73. a_2_1·b_7_15
  74. b_1_12·b_7_15 + b_1_16·b_3_2 + b_6_12·b_1_13 + b_6_11·b_3_4 + b_6_11·b_3_2
       + b_4_6·b_1_12·b_3_4
  75. a_8_5·a_1_0
  76. a_8_5·b_1_1
  77. b_5_82 + b_5_72 + b_5_52 + b_4_62·b_1_12 + b_2_2·b_4_62 + b_2_23·b_4_6
       + a_2_1·b_4_62 + a_2_1·b_2_24
  78. b_5_8·b_5_9 + b_5_7·b_5_9 + b_5_5·b_5_9 + b_5_5·b_5_8 + b_5_5·b_5_7 + b_5_52
       + b_4_6·b_1_1·b_5_9 + b_4_6·b_1_13·b_3_2 + b_4_62·b_1_12
  79. a_4_4·b_6_11
  80. b_5_7·b_5_8 + b_5_72 + b_5_52 + b_1_17·b_3_2 + b_6_11·b_1_1·b_3_2 + b_6_11·b_1_14
       + b_4_6·b_1_13·b_3_4 + b_4_6·b_1_13·b_3_2 + b_4_62·b_1_12 + b_2_2·b_4_62
       + b_2_22·b_6_11 + a_2_1·b_4_62 + a_2_1·b_2_2·b_6_11 + a_2_1·b_2_24
  81. b_5_92 + b_5_7·b_5_8 + b_1_17·b_3_2 + b_6_11·b_1_1·b_3_4 + b_6_11·b_1_14
       + b_4_6·b_1_1·b_5_7 + b_4_6·b_1_13·b_3_4 + b_4_6·b_1_13·b_3_2 + b_4_62·b_1_12
       + b_2_2·b_4_62 + b_2_22·b_6_11 + b_2_23·b_4_6 + b_2_25 + a_2_1·b_4_62
       + a_2_1·b_2_24
  82. b_5_52 + b_1_17·b_3_2 + b_6_12·b_1_14 + b_4_6·b_1_13·b_3_2 + b_4_6·b_1_16
       + b_4_62·b_1_12 + b_2_2·b_4_62 + a_2_1·b_4_62
  83. b_5_7·b_5_8 + b_5_72 + b_5_5·b_5_7 + b_4_6·b_1_1·b_5_7 + b_2_22·b_6_12 + b_2_23·b_4_6
       + b_2_25 + a_2_1·b_4_62 + a_2_1·b_2_2·b_6_11
  84. a_4_4·b_6_12 + a_2_1·b_4_62 + a_2_1·b_2_2·b_6_11
  85. b_5_8·b_5_9 + b_5_7·b_5_9 + b_5_7·b_5_8 + b_5_72 + b_5_5·b_5_8 + b_5_5·b_5_7 + b_5_52
       + b_1_17·b_3_2 + b_6_12·b_1_1·b_3_2 + b_6_11·b_1_14 + b_2_2·b_4_62 + b_2_22·b_6_11
       + a_2_1·b_4_62 + a_2_1·b_2_2·b_6_11 + a_2_1·b_2_24
  86. b_5_92 + b_5_7·b_5_8 + b_5_52 + b_3_2·b_7_14 + b_4_6·b_1_1·b_5_9 + b_4_6·b_1_1·b_5_7
       + b_4_6·b_1_13·b_3_4 + b_2_22·b_6_11 + b_2_23·b_4_6 + b_2_25 + a_2_1·b_2_24
  87. b_5_7·b_5_8 + b_5_72 + b_5_5·b_5_7 + b_3_3·b_7_14 + b_4_6·b_1_1·b_5_7 + b_2_2·b_4_62
       + b_2_22·b_6_11 + b_2_25 + a_2_1·b_2_2·b_6_11
  88. b_5_92 + b_5_8·b_5_9 + b_5_5·b_5_8 + b_5_52 + b_3_4·b_7_14 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_1·b_5_7 + b_4_62·b_1_12 + a_2_1·b_4_62 + a_2_1·b_2_2·b_6_11
  89. b_5_8·b_5_9 + b_5_72 + b_5_5·b_5_8 + b_5_52 + b_3_2·b_7_15 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_1·b_5_7 + b_4_6·b_1_13·b_3_2 + b_2_2·b_4_62 + b_2_23·b_4_6 + b_2_25
       + a_2_1·b_4_62
  90. b_5_7·b_5_8 + b_5_72 + b_5_5·b_5_7 + b_3_3·b_7_15 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_1·b_5_7 + b_4_6·b_1_13·b_3_4 + b_4_6·b_6_11 + b_2_2·b_4_62
       + b_2_22·b_6_11 + b_2_23·b_4_6 + a_2_1·b_2_24
  91. b_5_72 + b_5_52 + b_3_4·b_7_15 + b_4_6·b_1_1·b_5_7 + b_4_6·b_1_13·b_3_4
       + b_4_6·b_1_13·b_3_2 + b_4_62·b_1_12 + b_2_2·b_4_62 + b_2_23·b_4_6 + b_2_25
       + a_2_1·b_4_62 + a_2_1·b_2_2·b_6_11
  92. b_5_8·b_5_9 + b_5_7·b_5_9 + b_5_72 + b_5_5·b_5_8 + b_5_5·b_5_7 + b_1_17·b_3_2
       + b_4_6·b_1_1·b_5_7 + b_4_6·b_1_16 + b_4_62·b_1_12 + b_2_23·b_4_6 + b_2_25
       + a_2_1·b_2_2·b_6_11 + c_8_19·b_1_12
  93. b_5_7·b_5_8 + b_5_72 + b_5_5·b_5_8 + b_5_52 + b_4_6·b_1_1·b_5_7 + b_4_6·b_1_13·b_3_2
       + b_4_62·b_1_12 + b_2_2·b_4_62 + b_2_22·b_6_11 + b_2_23·b_4_6 + b_2_2·a_8_5
       + a_2_1·b_2_24
  94. a_2_1·a_8_5
  95. a_1_0·b_9_23
  96. b_5_92 + b_5_8·b_5_9 + b_5_5·b_5_8 + b_5_52 + b_1_1·b_9_23 + b_6_11·b_1_14
       + b_4_6·b_1_1·b_5_9 + b_4_6·b_1_13·b_3_4 + b_4_6·b_1_16 + a_2_1·b_2_2·b_6_11
  97. b_6_11·b_5_8 + b_6_11·b_5_7 + b_6_11·b_1_12·b_3_2 + b_2_22·b_4_6·b_3_3
       + a_2_1·b_2_22·b_5_8
  98. b_6_12·b_5_9 + b_6_12·b_5_8 + b_6_11·b_1_12·b_3_2 + b_4_6·b_1_12·b_5_7
       + b_4_6·b_1_14·b_3_2 + b_4_62·b_3_4 + b_4_62·b_3_3 + b_4_62·b_3_2 + b_4_62·b_1_13
       + b_2_24·b_3_3 + a_2_1·b_2_23·b_3_3
  99. b_6_12·b_5_5 + b_6_12·b_1_12·b_3_2 + b_6_11·b_5_5 + b_6_11·b_1_12·b_3_2
       + b_4_6·b_6_12·b_1_1 + b_4_6·b_6_11·b_1_1 + b_4_62·b_3_3 + b_2_2·b_4_6·b_5_5
       + b_2_23·b_5_5
  100. a_4_4·b_7_14 + a_2_1·b_2_22·b_5_8 + a_2_1·b_2_23·b_3_3
  101. b_6_12·b_5_8 + b_6_12·b_1_15 + b_6_11·b_5_5 + b_6_11·b_1_12·b_3_4
       + b_6_11·b_1_12·b_3_2 + b_6_11·b_1_15 + b_4_6·b_7_14 + b_4_6·b_1_12·b_5_7
       + b_4_6·b_1_14·b_3_2 + b_4_6·b_1_17 + b_4_6·b_6_12·b_1_1 + b_4_6·b_6_11·b_1_1
       + b_4_62·b_3_4 + b_4_62·b_3_3 + b_2_22·b_4_6·b_3_3 + b_2_23·b_5_5 + b_2_24·b_3_3
       + a_2_1·b_2_22·b_5_8
  102. b_6_12·b_5_8 + b_6_12·b_5_7 + b_6_12·b_1_12·b_3_2 + b_6_11·b_5_5 + b_6_11·b_1_12·b_3_2
       + b_4_6·b_6_11·b_1_1 + b_2_22·b_7_15 + b_2_23·b_5_8 + b_2_23·b_5_5 + b_2_24·b_3_3
       + a_2_1·b_2_22·b_5_8
  103. a_4_4·b_7_15
  104. b_1_18·b_3_2 + b_6_12·b_1_15 + b_6_11·b_5_9 + b_6_11·b_5_5 + b_6_11·b_1_12·b_3_2
       + b_6_11·b_1_15 + b_4_6·b_6_11·b_1_1 + c_8_19·b_1_13
  105. a_8_5·b_3_2
  106. b_6_11·b_5_5 + b_6_11·b_1_12·b_3_2 + b_4_6·b_6_11·b_1_1 + b_2_2·b_4_6·b_5_5
       + b_2_22·b_4_6·b_3_3 + b_2_23·b_5_5 + a_8_5·b_3_3 + a_2_1·b_2_22·b_5_8
       + a_2_1·b_2_23·b_3_3
  107. a_8_5·b_3_4
  108. b_6_11·b_5_5 + b_6_11·b_1_12·b_3_2 + b_4_6·b_6_11·b_1_1 + b_2_2·b_9_23
       + b_2_2·b_4_6·b_5_5 + b_2_22·b_4_6·b_3_3 + b_2_23·b_5_5 + a_2_1·b_2_23·b_3_3
       + b_2_2·c_8_19·a_1_0
  109. a_2_1·b_9_23
  110. b_1_12·b_9_23 + b_6_12·b_5_8 + b_6_12·b_5_7 + b_6_11·b_5_9 + b_6_11·b_5_8
       + b_6_11·b_1_15 + b_4_6·b_1_12·b_5_7 + b_4_6·b_1_14·b_3_2 + b_4_6·b_1_17
       + b_4_6·b_6_11·b_1_1 + a_2_1·b_2_23·b_3_3
  111. b_6_11·b_1_1·b_5_9 + b_6_11·b_1_13·b_3_4 + b_6_112 + b_2_22·b_4_62 + b_2_24·b_4_6
       + a_2_1·b_2_25
  112. b_6_12·b_1_13·b_3_2 + b_6_12·b_1_16 + b_6_122 + b_6_11·b_1_16 + b_4_6·b_1_18
       + b_4_6·b_6_12·b_1_12 + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_1·b_3_2 + b_4_62·b_1_14
       + b_4_63 + b_2_22·b_4_62 + b_2_24·b_4_6 + b_2_26 + a_2_1·b_2_25
  113. b_5_5·b_7_14 + b_6_12·b_1_13·b_3_2 + b_6_122 + b_6_11·b_1_13·b_3_4
       + b_4_6·b_1_1·b_7_14 + b_4_6·b_1_15·b_3_2 + b_4_6·b_6_11·b_1_12
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14 + b_4_63 + b_2_2·b_4_6·b_6_12
       + b_2_2·b_4_6·b_6_11 + b_2_22·b_4_62 + b_2_23·b_6_12 + b_2_23·b_6_11 + b_2_24·b_4_6
       + a_2_1·b_4_6·b_6_12
  114. b_5_9·b_7_14 + b_5_7·b_7_14 + b_6_12·b_1_13·b_3_2 + b_6_122 + b_6_11·b_1_1·b_5_7
       + b_6_11·b_1_13·b_3_4 + b_6_11·b_1_13·b_3_2 + b_4_6·b_1_1·b_7_15
       + b_4_6·b_1_13·b_5_7 + b_4_6·b_1_15·b_3_2 + b_4_62·b_1_1·b_3_2 + b_4_63
       + b_2_2·b_4_6·b_6_12 + b_2_2·b_4_6·b_6_11 + a_2_1·b_2_22·b_6_11
  115. b_5_9·b_7_15 + b_5_8·b_7_15 + b_5_7·b_7_14 + b_6_11·b_1_1·b_5_7 + b_6_11·b_1_13·b_3_4
       + b_6_11·b_6_12 + b_4_6·b_1_1·b_7_14 + b_4_6·b_1_15·b_3_2 + b_4_62·b_1_1·b_3_4
       + b_4_62·b_1_14 + b_2_2·b_4_6·b_6_12 + b_2_23·b_6_11 + b_2_24·b_4_6 + b_2_26
  116. b_5_9·b_7_14 + b_5_8·b_7_15 + b_5_7·b_7_15 + b_5_7·b_7_14 + b_5_5·b_7_15
       + b_6_12·b_1_13·b_3_2 + b_6_122 + b_6_11·b_1_1·b_5_7 + b_6_11·b_6_12
       + b_4_6·b_1_1·b_7_14 + b_4_6·b_1_15·b_3_2 + b_4_6·b_6_11·b_1_12
       + b_4_62·b_1_1·b_3_2 + b_4_63 + b_2_23·b_6_11 + a_2_1·b_4_6·b_6_12 + a_2_1·b_2_25
  117. b_5_8·b_7_15 + b_5_8·b_7_14 + b_5_7·b_7_15 + b_5_7·b_7_14 + b_6_12·b_1_13·b_3_2
       + b_6_12·b_1_16 + b_6_11·b_1_1·b_5_7 + b_4_6·b_1_13·b_5_7 + b_4_6·b_1_15·b_3_2
       + b_4_62·b_1_14 + b_2_22·b_4_62 + b_2_23·b_6_11 + a_2_1·b_2_25 + c_8_19·b_1_14
  118. b_5_9·b_7_14 + b_5_8·b_7_15 + b_5_8·b_7_14 + b_5_7·b_7_15 + b_5_7·b_7_14 + b_6_122
       + b_6_11·b_1_13·b_3_4 + b_4_6·b_1_13·b_5_7 + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14
       + b_4_63 + b_2_2·b_4_6·b_6_12 + b_2_2·b_4_6·b_6_11 + b_2_23·b_6_12 + b_2_24·b_4_6
       + a_2_1·b_4_6·b_6_12 + a_2_1·b_2_22·b_6_11 + a_2_1·b_2_25 + c_8_19·b_1_1·b_3_2
  119. b_5_8·b_7_15 + b_5_8·b_7_14 + b_5_7·b_7_14 + b_6_12·b_1_13·b_3_2 + b_6_11·b_1_1·b_5_7
       + b_6_11·b_1_13·b_3_2 + b_6_112 + b_4_6·b_1_13·b_5_7 + b_4_6·b_1_15·b_3_2
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14 + b_2_2·b_4_6·b_6_11 + b_2_22·b_4_62
       + b_2_23·b_6_12 + b_2_24·b_4_6 + b_2_26 + a_2_1·b_2_22·b_6_11 + a_2_1·b_2_25
       + c_8_19·b_1_1·b_3_4
  120. b_5_8·b_7_14 + b_5_7·b_7_14 + b_6_12·b_1_13·b_3_2 + b_6_122 + b_6_11·b_1_13·b_3_4
       + b_4_6·b_1_15·b_3_2 + b_4_6·b_6_11·b_1_12 + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14
       + b_4_63 + b_2_2·b_4_6·b_6_11 + b_2_22·b_4_62 + b_2_23·b_6_12 + b_2_24·b_4_6
       + b_2_22·a_8_5 + a_2_1·b_2_22·b_6_11 + a_2_1·b_2_25
  121. a_4_4·a_8_5
  122. b_5_8·b_7_14 + b_5_7·b_7_14 + b_6_12·b_1_13·b_3_2 + b_6_122 + b_6_11·b_1_13·b_3_2
       + b_6_11·b_6_12 + b_4_6·b_1_1·b_7_14 + b_4_6·b_1_13·b_5_7 + b_4_6·b_1_15·b_3_2
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14 + b_4_63 + b_2_2·b_4_6·b_6_12
       + b_2_2·b_4_6·b_6_11 + b_2_24·b_4_6 + b_2_26 + b_4_6·a_8_5 + a_2_1·b_2_22·b_6_11
       + a_2_1·b_2_25
  123. b_5_9·b_7_14 + b_5_7·b_7_14 + b_3_2·b_9_23 + b_6_11·b_1_13·b_3_2
       + b_4_6·b_6_11·b_1_12 + b_4_62·b_1_1·b_3_4 + b_2_2·b_4_6·b_6_12 + b_2_2·b_4_6·b_6_11
       + b_2_22·b_4_62 + b_2_24·b_4_6 + b_2_26 + a_2_1·b_2_22·b_6_11 + a_2_1·b_2_25
  124. b_3_3·b_9_23 + b_6_11·b_1_13·b_3_4 + b_6_11·b_1_13·b_3_2 + b_6_11·b_6_12
       + b_4_6·b_1_1·b_7_14 + b_4_6·b_1_13·b_5_7 + b_4_6·b_6_11·b_1_12 + b_2_2·b_4_6·b_6_12
       + b_2_22·b_4_62 + b_2_23·b_6_12 + b_2_26 + a_2_1·b_4_6·b_6_12
       + a_2_1·b_2_22·b_6_11 + a_2_1·b_2_25 + a_2_1·b_2_2·c_8_19
  125. b_5_9·b_7_14 + b_3_4·b_9_23 + b_6_11·b_1_1·b_5_7 + b_6_11·b_1_13·b_3_4
       + b_6_11·b_1_13·b_3_2 + b_4_6·b_1_13·b_5_7 + b_4_6·b_1_15·b_3_2
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_1·b_3_2 + b_4_62·b_1_14 + b_2_2·b_4_6·b_6_12
       + b_2_2·b_4_6·b_6_11 + b_2_23·b_6_12 + b_2_23·b_6_11 + b_2_26 + a_2_1·b_4_6·b_6_12
       + a_2_1·b_2_22·b_6_11 + a_2_1·b_2_25
  126. b_6_12·b_7_14 + b_6_12·b_1_17 + b_6_11·b_7_14 + b_6_11·b_1_12·b_5_7
       + b_4_6·b_6_12·b_1_13 + b_4_6·b_6_11·b_3_4 + b_4_62·b_5_9 + b_2_22·b_4_6·b_5_5
       + b_2_25·b_3_3 + a_2_1·b_2_23·b_5_8 + a_2_1·b_2_24·b_3_3 + c_8_19·b_1_12·b_3_2
       + c_8_19·b_1_15
  127. b_6_122·b_1_1 + b_6_11·b_7_15 + b_6_11·b_7_14 + b_6_11·b_1_17 + b_6_11·b_6_12·b_1_1
       + b_4_6·b_1_19 + b_4_6·b_6_12·b_3_2 + b_4_6·b_6_12·b_1_13 + b_4_6·b_6_11·b_3_4
       + b_4_62·b_1_12·b_3_2 + b_4_62·b_1_15 + b_2_2·b_4_62·b_3_3 + b_2_23·b_7_15
       + b_2_23·b_4_6·b_3_3 + b_2_24·b_5_8 + b_2_24·b_5_5 + b_2_25·b_3_3
       + a_2_1·b_2_23·b_5_8 + c_8_19·b_1_12·b_3_4 + c_8_19·b_1_15
  128. b_2_23·b_7_15 + a_8_5·b_5_8
  129. b_6_12·b_7_14 + b_6_122·b_1_1 + b_6_11·b_1_12·b_5_7 + b_6_11·b_1_14·b_3_2
       + b_6_112·b_1_1 + b_4_6·b_1_16·b_3_2 + b_4_6·b_6_11·b_3_4 + b_4_6·b_6_11·b_1_13
       + b_4_62·b_5_9 + b_4_62·b_1_12·b_3_4 + b_4_62·b_1_12·b_3_2 + b_4_62·b_1_15
       + b_4_63·b_1_1 + b_2_2·b_4_6·b_7_15 + b_2_2·b_4_62·b_3_3 + b_2_22·b_4_6·b_5_5
       + b_2_23·b_4_6·b_3_3 + b_2_24·b_5_8 + b_2_24·b_5_5 + b_2_2·a_8_5·b_3_3
       + a_2_1·b_2_24·b_3_3
  130. b_2_2·b_4_6·b_7_15 + a_8_5·b_5_9
  131. b_6_12·b_7_14 + b_6_122·b_1_1 + b_6_11·b_1_12·b_5_7 + b_6_11·b_1_14·b_3_2
       + b_6_112·b_1_1 + b_4_6·b_1_16·b_3_2 + b_4_6·b_6_11·b_3_4 + b_4_6·b_6_11·b_1_13
       + b_4_62·b_5_9 + b_4_62·b_1_12·b_3_4 + b_4_62·b_1_12·b_3_2 + b_4_62·b_1_15
       + b_4_63·b_1_1 + b_2_2·b_4_6·b_7_15 + b_2_2·b_4_62·b_3_3 + b_2_22·b_4_6·b_5_5
       + b_2_23·b_4_6·b_3_3 + b_2_24·b_5_8 + b_2_24·b_5_5 + a_8_5·b_5_7 + a_2_1·b_2_24·b_3_3
  132. b_2_2·b_4_6·b_7_15 + a_8_5·b_5_5
  133. a_4_4·b_9_23
  134. b_6_12·b_7_15 + b_6_12·b_7_14 + b_6_12·b_1_17 + b_6_122·b_1_1 + b_6_11·b_1_14·b_3_2
       + b_6_11·b_1_17 + b_6_11·b_6_12·b_1_1 + b_6_112·b_1_1 + b_4_6·b_9_23
       + b_4_6·b_1_16·b_3_2 + b_4_6·b_1_19 + b_4_6·b_6_12·b_3_2 + b_4_62·b_5_9
       + b_4_62·b_1_12·b_3_4 + b_4_63·b_1_1 + b_2_2·b_4_6·b_7_15 + b_2_2·b_4_62·b_3_3
       + b_2_22·b_4_6·b_5_5 + b_2_23·b_4_6·b_3_3 + b_2_24·b_5_8 + b_2_24·b_5_5
       + a_2_1·b_2_24·b_3_3
  135. b_7_142 + b_6_11·b_1_13·b_5_7 + b_6_11·b_1_15·b_3_2 + b_6_11·b_1_18
       + b_6_11·b_6_12·b_1_12 + b_6_112·b_1_12 + b_4_6·b_1_17·b_3_2 + b_4_6·b_1_110
       + b_4_6·b_6_11·b_1_1·b_3_4 + b_4_6·b_6_11·b_1_1·b_3_2 + b_4_62·b_1_13·b_3_2
       + b_2_2·b_4_63 + b_2_25·b_4_6 + b_2_27 + a_2_1·b_4_63 + a_2_1·b_2_23·b_6_11
       + c_8_19·b_1_13·b_3_4 + c_8_19·b_1_16 + b_4_6·c_8_19·b_1_12
  136. b_7_152 + b_7_142 + b_6_11·b_1_1·b_7_15 + b_6_11·b_1_13·b_5_7
       + b_6_11·b_1_15·b_3_2 + b_4_6·b_6_12·b_1_1·b_3_2 + b_4_6·b_6_11·b_1_1·b_3_4
       + b_4_6·b_6_11·b_1_1·b_3_2 + b_4_6·b_6_11·b_1_14 + b_4_62·b_1_1·b_5_7
       + b_4_62·b_1_13·b_3_4 + b_4_62·b_1_16 + b_2_2·b_4_63 + b_2_25·b_4_6 + b_2_27
       + a_2_1·b_4_63 + a_2_1·b_2_23·b_6_11 + c_8_19·b_1_1·b_5_7 + c_8_19·b_1_13·b_3_2
  137. b_4_62·b_1_1·b_5_9 + b_4_62·b_1_13·b_3_4 + b_4_62·b_6_11 + b_2_2·b_4_63
       + b_2_22·b_4_6·b_6_12 + b_2_23·b_4_62 + b_2_24·b_6_12 + b_2_24·b_6_11
       + b_2_25·b_4_6 + b_2_27 + b_6_12·a_8_5 + a_2_1·b_2_23·b_6_11 + a_2_1·b_2_26
  138. b_2_22·b_4_6·b_6_11 + b_2_23·b_4_62 + b_2_24·b_6_12 + b_2_24·b_6_11 + b_2_27
       + b_6_11·a_8_5 + b_2_2·b_4_6·a_8_5 + b_2_23·a_8_5 + a_2_1·b_2_23·b_6_11
       + a_2_1·b_2_26
  139. b_7_152 + b_5_8·b_9_23 + b_6_11·b_1_1·b_7_15 + b_6_11·b_1_13·b_5_7 + b_6_11·b_1_18
       + b_6_11·b_6_12·b_1_12 + b_4_6·b_1_110 + b_4_6·b_6_11·b_1_1·b_3_4
       + b_4_6·b_6_11·b_1_1·b_3_2 + b_4_6·b_6_11·b_1_14 + b_4_62·b_1_1·b_5_9
       + b_4_62·b_1_1·b_5_7 + b_4_62·b_1_13·b_3_2 + b_2_22·b_4_6·b_6_11 + b_2_23·b_4_62
       + b_2_24·b_6_12 + b_2_24·b_6_11 + b_2_27 + a_2_1·b_2_23·b_6_11 + c_8_19·b_1_1·b_5_9
       + c_8_19·b_1_13·b_3_2 + c_8_19·b_1_16 + b_2_2·a_4_4·c_8_19 + a_2_1·b_2_22·c_8_19
  140. b_7_152 + b_7_14·b_7_15 + b_7_142 + b_6_11·b_1_1·b_7_15 + b_6_11·b_1_13·b_5_7
       + b_6_112·b_1_12 + b_4_6·b_1_1·b_9_23 + b_4_6·b_6_12·b_1_1·b_3_2
       + b_4_6·b_6_11·b_1_1·b_3_4 + b_4_62·b_6_11 + b_4_63·b_1_12 + b_2_22·b_4_6·b_6_12
       + b_2_22·b_4_6·b_6_11 + b_2_27 + b_6_11·a_8_5 + b_2_23·a_8_5 + a_2_1·b_2_23·b_6_11
       + c_8_19·b_1_1·b_5_9 + c_8_19·b_1_13·b_3_4 + c_8_19·b_1_13·b_3_2
  141. b_7_14·b_7_15 + b_5_9·b_9_23 + b_6_11·b_1_1·b_7_15 + b_6_11·b_1_15·b_3_2
       + b_6_11·b_6_12·b_1_12 + b_6_112·b_1_12 + b_4_6·b_1_17·b_3_2
       + b_4_6·b_6_12·b_1_14 + b_4_6·b_6_11·b_1_1·b_3_4 + b_4_62·b_1_1·b_5_9
       + b_4_62·b_1_13·b_3_4 + b_6_11·a_8_5 + b_2_23·a_8_5
  142. b_7_152 + b_5_7·b_9_23 + b_6_11·b_1_18 + b_6_11·b_6_12·b_1_12 + b_6_112·b_1_12
       + b_4_6·b_1_17·b_3_2 + b_4_6·b_1_110 + b_4_6·b_6_11·b_1_1·b_3_4
       + b_4_6·b_6_11·b_1_1·b_3_2 + b_4_62·b_1_1·b_5_9 + b_4_62·b_1_1·b_5_7
       + b_4_62·b_1_13·b_3_4 + b_4_62·b_1_13·b_3_2 + b_4_62·b_1_16
       + b_2_22·b_4_6·b_6_11 + b_2_23·b_4_62 + b_2_24·b_6_12 + b_2_24·b_6_11 + b_2_27
       + b_6_11·a_8_5 + c_8_19·b_1_1·b_5_9 + c_8_19·b_1_13·b_3_4 + c_8_19·b_1_16
       + a_2_1·b_2_22·c_8_19
  143. b_7_152 + b_7_14·b_7_15 + b_7_142 + b_5_5·b_9_23 + b_4_6·b_1_17·b_3_2
       + b_4_6·b_6_12·b_1_1·b_3_2 + b_4_6·b_6_11·b_1_1·b_3_4 + b_4_6·b_6_11·b_1_14
       + b_4_62·b_1_1·b_5_9 + b_4_62·b_1_16 + b_4_63·b_1_12 + b_2_2·b_4_63
       + b_2_25·b_4_6 + b_2_27 + b_6_11·a_8_5 + b_2_23·a_8_5 + a_2_1·b_4_63
       + a_2_1·b_2_23·b_6_11 + c_8_19·b_1_1·b_5_9
  144. a_8_5·b_7_15
  145. a_8_5·b_7_14 + b_4_6·a_8_5·b_3_3 + b_2_2·a_8_5·b_5_5 + b_2_22·a_8_5·b_3_3
  146. b_6_11·b_9_23 + b_6_11·b_1_19 + b_6_112·b_3_4 + b_6_112·b_3_2 + b_4_6·b_1_111
       + b_4_6·b_6_12·b_1_15 + b_4_6·b_6_11·b_5_7 + b_4_62·b_6_12·b_1_1
       + b_4_62·b_6_11·b_1_1 + b_4_63·b_3_2 + b_2_22·b_4_62·b_3_3 + b_2_23·b_4_6·b_5_5
       + b_2_24·b_4_6·b_3_3 + b_2_25·b_5_5 + b_4_6·a_8_5·b_3_3 + b_2_22·a_8_5·b_3_3
       + c_8_19·b_1_12·b_5_7 + c_8_19·b_1_14·b_3_2 + c_8_19·b_1_17 + b_6_11·c_8_19·b_1_1
       + b_4_6·c_8_19·b_1_13 + a_2_1·c_8_19·b_5_8 + a_2_1·b_2_2·c_8_19·b_3_3
  147. b_6_12·b_9_23 + b_6_11·b_1_19 + b_6_11·b_6_12·b_3_2 + b_6_11·b_6_12·b_1_13
       + b_6_112·b_3_4 + b_6_112·b_3_2 + b_4_6·b_1_111 + b_4_6·b_6_12·b_1_12·b_3_2
       + b_4_6·b_6_12·b_1_15 + b_4_6·b_6_11·b_5_9 + b_4_6·b_6_11·b_5_7
       + b_4_6·b_6_11·b_1_12·b_3_4 + b_4_62·b_7_15 + b_4_62·b_1_12·b_5_7 + b_4_63·b_3_2
       + b_2_2·b_4_62·b_5_5 + b_2_24·b_4_6·b_3_3 + b_2_25·b_5_5 + a_8_5·b_7_14
       + b_2_22·a_8_5·b_3_3 + a_2_1·b_2_24·b_5_8 + c_8_19·b_1_14·b_3_2 + c_8_19·b_1_17
       + b_6_12·c_8_19·b_1_1 + b_4_6·c_8_19·b_3_2 + b_4_6·c_8_19·b_1_13 + a_2_1·c_8_19·b_5_8
  148. a_8_52
  149. b_7_14·b_9_23 + b_6_11·b_6_12·b_1_1·b_3_2 + b_6_11·b_6_12·b_1_14 + b_6_112·b_1_14
       + b_4_6·b_6_122 + b_4_6·b_6_11·b_1_16 + b_4_6·b_6_112 + b_4_62·b_1_1·b_7_15
       + b_4_62·b_1_1·b_7_14 + b_4_62·b_1_15·b_3_2 + b_4_62·b_6_12·b_1_12
       + b_4_62·b_6_11·b_1_12 + b_4_63·b_1_14 + b_4_64 + b_2_26·b_4_6 + b_4_62·a_8_5
       + b_2_2·b_6_12·a_8_5 + b_2_2·b_6_11·a_8_5 + b_2_22·b_4_6·a_8_5 + a_2_1·b_4_62·b_6_12
       + a_2_1·b_2_24·b_6_11 + a_2_1·b_2_27 + c_8_19·b_1_13·b_5_7 + b_6_12·c_8_19·b_1_12
       + b_4_6·c_8_19·b_1_1·b_3_4 + b_4_6·c_8_19·b_1_14 + a_2_1·b_2_23·c_8_19
  150. b_7_15·b_9_23 + b_6_11·b_6_12·b_1_1·b_3_2 + b_6_112·b_1_1·b_3_2
       + b_4_6·b_6_12·b_1_16 + b_4_6·b_6_122 + b_4_6·b_6_11·b_1_1·b_5_7
       + b_4_6·b_6_11·b_1_13·b_3_2 + b_4_6·b_6_112 + b_4_62·b_1_1·b_7_15
       + b_4_62·b_1_1·b_7_14 + b_4_63·b_1_14 + b_4_64 + b_2_26·b_4_6
       + c_8_19·b_1_1·b_7_14 + b_4_6·c_8_19·b_1_1·b_3_4
  151. a_8_5·b_9_23
  152. b_9_232 + b_6_11·b_6_12·b_1_16 + b_6_112·b_1_1·b_5_7 + b_6_113
       + b_4_6·b_6_11·b_1_1·b_7_15 + b_4_6·b_6_11·b_1_1·b_7_14 + b_4_6·b_6_11·b_1_13·b_5_7
       + b_4_6·b_6_11·b_6_12·b_1_12 + b_4_6·b_6_112·b_1_12 + b_4_62·b_1_17·b_3_2
       + b_4_62·b_6_11·b_1_1·b_3_4 + b_4_62·b_6_11·b_1_1·b_3_2 + b_4_62·b_6_11·b_1_14
       + b_4_63·b_1_1·b_5_7 + b_4_63·b_1_13·b_3_4 + b_2_23·b_4_63 + b_2_24·b_4_6·b_6_12
       + b_2_27·b_4_6 + b_2_22·b_6_12·a_8_5 + b_2_22·b_6_11·a_8_5 + b_2_23·b_4_6·a_8_5
       + b_2_25·a_8_5 + a_2_1·b_2_25·b_6_11 + b_6_12·c_8_19·b_1_1·b_3_2
       + b_6_12·c_8_19·b_1_14 + b_6_11·c_8_19·b_1_1·b_3_4 + b_6_11·c_8_19·b_1_1·b_3_2
       + b_6_11·c_8_19·b_1_14 + b_4_6·c_8_19·b_1_1·b_5_7 + b_4_6·c_8_19·b_1_13·b_3_4

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_19, a Duflot regular element of degree 8
    2. b_1_1·b_3_4 + b_1_14 + b_4_6 + b_2_22, an element of degree 4
    3. b_1_13·b_3_4 + b_4_6·b_1_12 + b_2_2·b_4_6, an element of degree 6
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 9, 15].
  • 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_1 → 0, an element of degree 2
  4. b_2_2 → 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. a_4_4 → 0, an element of degree 4
  9. b_4_6 → 0, an element of degree 4
  10. b_5_5 → 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_5_9 → 0, an element of degree 5
  14. b_6_11 → 0, an element of degree 6
  15. b_6_12 → 0, an element of degree 6
  16. b_7_14 → 0, an element of degree 7
  17. b_7_15 → 0, an element of degree 7
  18. a_8_5 → 0, an element of degree 8
  19. c_8_19 → c_1_08, an element of degree 8
  20. b_9_23 → 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_1 → 0, an element of degree 2
  4. b_2_2 → 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. a_4_4 → 0, an element of degree 4
  9. b_4_6 → c_1_24 + c_1_12·c_1_22 + c_1_0·c_1_13 + c_1_02·c_1_12, an element of degree 4
  10. b_5_5 → c_1_1·c_1_24 + c_1_14·c_1_2 + c_1_0·c_1_14 + c_1_02·c_1_13, an element of degree 5
  11. b_5_7 → c_1_13·c_1_22 + c_1_14·c_1_2 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_5_8 → c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  13. b_5_9 → c_1_1·c_1_24 + 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_0·c_1_14 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_1, an element of degree 5
  14. b_6_11 → 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_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_6_12 → c_1_26 + c_1_1·c_1_25 + c_1_12·c_1_24 + c_1_13·c_1_23 + c_1_14·c_1_22
       + 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_02·c_1_14, an element of degree 6
  16. b_7_14 → c_1_1·c_1_26 + c_1_12·c_1_25 + c_1_13·c_1_24 + c_1_14·c_1_23
       + c_1_0·c_1_12·c_1_24 + c_1_0·c_1_15·c_1_2 + c_1_02·c_1_1·c_1_24
       + c_1_02·c_1_13·c_1_22 + 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_7_15 → 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_0·c_1_16 + c_1_02·c_1_1·c_1_24 + c_1_02·c_1_13·c_1_22 + c_1_03·c_1_14
       + c_1_05·c_1_12 + c_1_06·c_1_1, an element of degree 7
  18. a_8_5 → 0, an element of degree 8
  19. c_8_19 → 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_13·c_1_24 + c_1_0·c_1_16·c_1_2 + c_1_0·c_1_17
       + c_1_03·c_1_15 + c_1_04·c_1_24 + c_1_04·c_1_13·c_1_2 + c_1_04·c_1_14
       + c_1_05·c_1_13 + c_1_06·c_1_12 + c_1_08, an element of degree 8
  20. b_9_23 → c_1_1·c_1_28 + c_1_13·c_1_26 + c_1_14·c_1_25 + 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_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_16·c_1_2 + c_1_03·c_1_14·c_1_22 + c_1_03·c_1_15·c_1_2
       + c_1_03·c_1_16 + c_1_05·c_1_12·c_1_22 + c_1_05·c_1_13·c_1_2
       + c_1_05·c_1_14 + c_1_06·c_1_1·c_1_22 + c_1_06·c_1_12·c_1_2 + c_1_06·c_1_13, 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_1 → 0, an element of degree 2
  4. b_2_2 → c_1_22 + c_1_12, an element of degree 2
  5. b_3_2 → 0, an element of degree 3
  6. b_3_3 → c_1_23 + c_1_13, an element of degree 3
  7. b_3_4 → 0, an element of degree 3
  8. a_4_4 → 0, an element of degree 4
  9. b_4_6 → c_1_12·c_1_22, an element of degree 4
  10. b_5_5 → c_1_12·c_1_23 + c_1_13·c_1_22, an element of degree 5
  11. b_5_7 → c_1_25 + c_1_12·c_1_23 + c_1_13·c_1_22 + c_1_15, an element of degree 5
  12. b_5_8 → c_1_25 + c_1_1·c_1_24 + c_1_14·c_1_2 + c_1_15, an element of degree 5
  13. b_5_9 → c_1_12·c_1_23 + c_1_13·c_1_22, an element of degree 5
  14. b_6_11 → c_1_1·c_1_25 + c_1_12·c_1_24 + c_1_14·c_1_22 + c_1_15·c_1_2, an element of degree 6
  15. b_6_12 → c_1_26 + c_1_1·c_1_25 + c_1_13·c_1_23 + c_1_15·c_1_2 + c_1_16, an element of degree 6
  16. b_7_14 → c_1_27 + c_1_17, an element of degree 7
  17. b_7_15 → 0, an element of degree 7
  18. a_8_5 → 0, an element of degree 8
  19. c_8_19 → c_1_28 + c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_16·c_1_22 + c_1_18
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22 + 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
  20. b_9_23 → 0, 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