Cohomology of group number 53 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 1.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t2  −  t  +  1)
    (t  −  1)3 · (t2  +  1)
  • The a-invariants are -∞,-3,-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 21 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. a_3_2, a nilpotent 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_2, a nilpotent element of degree 4
  9. b_4_6, an element of degree 4
  10. b_4_7, an element of degree 4
  11. a_5_6, a nilpotent element of degree 5
  12. b_5_9, an element of degree 5
  13. b_5_10, an element of degree 5
  14. a_6_6, a nilpotent element of degree 6
  15. b_6_13, an element of degree 6
  16. a_7_8, a nilpotent element of degree 7
  17. b_7_16, an element of degree 7
  18. b_7_17, an element of degree 7
  19. a_8_8, a nilpotent element of degree 8
  20. c_8_22, a Duflot regular element of degree 8
  21. b_9_27, 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 169 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·a_1_0
  6. a_2_12
  7. b_2_2·b_1_12
  8. a_1_0·a_3_2
  9. a_1_0·b_3_3
  10. a_1_0·b_3_4
  11. b_1_1·b_3_4 + a_2_1·b_2_2
  12. a_2_1·a_3_2
  13. b_2_22·b_1_1 + a_2_1·b_3_3
  14. b_2_2·b_3_4 + b_2_2·b_3_3 + b_2_2·a_3_2
  15. b_2_2·a_3_2 + a_2_1·b_3_4
  16. a_4_2·a_1_0
  17. b_2_22·b_1_1 + a_4_2·b_1_1 + b_2_2·a_3_2
  18. b_2_22·b_1_1 + b_4_6·a_1_0 + b_2_2·a_3_2
  19. b_4_7·a_1_0
  20. a_3_22
  21. a_3_2·b_3_4 + a_2_1·b_2_22
  22. b_3_42 + b_2_23 + a_2_1·b_2_22
  23. b_3_3·b_3_4 + b_2_23
  24. a_2_1·a_4_2
  25. b_2_2·a_4_2 + a_2_1·b_4_6 + a_2_1·b_2_22
  26. b_1_13·b_3_3 + b_4_6·b_1_12 + a_3_2·b_3_3 + b_1_13·a_3_2 + a_2_1·b_2_22
  27. b_3_32 + b_4_7·b_1_12 + b_2_23 + a_2_1·b_2_22
  28. a_1_0·a_5_6
  29. b_1_1·a_5_6
  30. a_1_0·b_5_9
  31. a_1_0·b_5_10
  32. b_1_1·b_5_10 + b_1_1·b_5_9 + b_2_2·a_4_2 + a_2_1·b_2_22
  33. a_4_2·a_3_2
  34. a_4_2·b_3_4 + a_4_2·b_3_3
  35. b_1_1·a_3_2·b_3_3 + b_4_6·a_3_2 + a_4_2·b_3_4 + a_2_1·b_2_2·b_3_3
  36. b_2_2·b_4_6·b_1_1 + a_4_2·b_3_4 + a_2_1·b_2_2·b_3_3
  37. b_4_7·b_1_13 + b_4_6·b_3_4 + b_4_6·b_3_3 + b_2_2·b_4_7·b_1_1 + b_1_1·a_3_2·b_3_3
       + b_4_7·a_3_2 + a_4_2·b_3_4 + a_2_1·b_2_2·b_3_3
  38. b_4_7·b_1_13 + b_4_6·b_3_4 + b_4_6·b_3_3 + b_1_1·a_3_2·b_3_3 + b_4_7·a_3_2 + a_4_2·b_3_4
       + b_2_2·a_5_6 + a_2_1·b_2_2·b_3_3
  39. a_2_1·a_5_6
  40. b_4_7·b_1_13 + b_4_6·b_3_4 + b_4_6·b_3_3 + b_1_1·a_3_2·b_3_3 + b_4_7·a_3_2 + a_4_2·b_3_4
       + a_2_1·b_5_9 + a_2_1·b_2_2·b_3_3
  41. b_4_7·b_1_13 + b_4_6·b_3_3 + b_2_2·b_5_10 + b_2_2·b_5_9 + b_1_1·a_3_2·b_3_3
       + b_4_7·a_3_2 + a_4_2·b_3_4 + a_2_1·b_2_2·b_3_3
  42. b_4_7·b_1_13 + b_4_6·b_3_4 + b_4_6·b_3_3 + b_1_1·a_3_2·b_3_3 + b_4_7·a_3_2
       + a_2_1·b_5_10
  43. a_6_6·a_1_0
  44. b_4_7·b_1_13 + b_4_6·b_3_4 + b_4_6·b_3_3 + a_6_6·b_1_1 + a_4_2·b_3_4 + a_2_1·b_2_2·b_3_3
  45. b_6_13·a_1_0
  46. b_6_13·b_1_1 + b_4_7·b_3_3 + b_4_7·b_1_13 + b_4_6·b_1_13 + b_2_2·b_5_9 + b_4_7·a_3_2
  47. a_4_22
  48. b_4_6·b_1_1·b_3_3 + b_4_62 + b_2_22·b_4_7 + b_4_7·b_1_1·a_3_2 + b_4_6·b_1_1·a_3_2
       + a_2_1·b_2_2·b_4_6 + a_2_1·b_2_23
  49. a_4_2·b_4_6 + a_2_1·b_2_2·b_4_7 + a_2_1·b_2_2·b_4_6
  50. a_3_2·a_5_6
  51. b_3_4·a_5_6 + a_4_2·b_4_6 + a_2_1·b_2_2·b_4_6
  52. b_3_3·a_5_6 + a_4_2·b_4_6 + a_2_1·b_2_2·b_4_6
  53. b_2_2·b_1_1·b_5_9 + a_4_2·b_4_6 + a_2_1·b_2_2·b_4_6
  54. a_3_2·b_5_10 + a_3_2·b_5_9 + a_2_1·b_2_2·b_4_6
  55. b_3_4·b_5_10 + b_3_4·b_5_9 + b_2_22·b_4_6 + a_4_2·b_4_6
  56. b_3_3·b_5_10 + b_3_3·b_5_9 + b_2_22·b_4_6 + a_4_2·b_4_6 + a_2_1·b_2_2·b_4_6
  57. b_3_4·b_5_9 + b_4_6·b_1_1·b_3_3 + b_4_62 + b_4_7·b_1_1·a_3_2 + b_4_6·b_1_1·a_3_2
       + a_4_2·b_4_7 + b_2_2·a_6_6
  58. a_2_1·a_6_6
  59. b_3_4·b_5_9 + b_4_6·b_1_1·b_3_3 + b_4_62 + b_4_7·b_1_1·a_3_2 + b_4_6·b_1_1·a_3_2
       + a_4_2·b_4_6 + a_2_1·b_6_13 + a_2_1·b_2_23
  60. a_1_0·a_7_8
  61. a_3_2·b_5_9 + b_1_1·a_7_8 + a_4_2·b_4_6 + a_2_1·b_2_2·b_4_6
  62. a_1_0·b_7_16
  63. b_3_3·b_5_9 + b_1_1·b_7_16 + b_1_13·b_5_9 + b_4_7·b_1_1·b_3_3 + b_4_6·b_1_1·b_3_3
       + b_4_62 + a_3_2·b_5_9 + b_4_7·b_1_1·a_3_2 + a_2_1·b_2_2·b_4_6 + a_2_1·b_2_23
  64. a_1_0·b_7_17
  65. b_3_4·b_5_9 + b_1_1·b_7_17 + b_4_6·b_1_14 + b_4_62 + a_3_2·b_5_9 + b_4_7·b_1_1·a_3_2
       + b_4_6·b_1_1·a_3_2 + a_4_2·b_4_7 + a_4_2·b_4_6 + a_2_1·b_2_2·b_4_6 + a_2_1·b_2_23
  66. a_4_2·a_5_6
  67. b_4_6·a_5_6 + a_4_2·b_5_9 + a_2_1·b_2_2·b_5_9
  68. a_4_2·b_5_10 + a_4_2·b_5_9 + a_2_1·b_2_2·b_5_10
  69. b_4_6·b_5_10 + b_4_6·b_5_9 + b_2_2·b_4_7·b_3_3 + a_4_2·b_5_9 + a_2_1·b_2_22·b_3_3
  70. a_6_6·a_3_2
  71. b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9 + a_6_6·b_3_4 + b_4_6·a_5_6 + a_4_2·b_5_10 + a_4_2·b_5_9
       + a_2_1·b_2_22·b_3_3
  72. b_4_7·b_1_12·b_3_3 + b_4_6·b_4_7·b_1_1 + b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9
       + a_6_6·b_3_3 + a_4_2·b_5_10 + a_4_2·b_5_9 + a_2_1·b_2_22·b_3_3
  73. b_4_7·b_1_12·b_3_3 + b_4_6·b_4_7·b_1_1 + b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9
       + b_6_13·a_3_2 + b_4_6·b_1_12·a_3_2 + a_4_2·b_5_9
  74. b_6_13·b_3_4 + b_6_13·b_3_3 + b_4_72·b_1_1 + b_4_6·b_4_7·b_1_1 + b_4_62·b_1_1
       + b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9 + b_4_7·a_5_6 + b_4_6·a_5_6 + b_4_6·b_1_12·a_3_2
  75. b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9 + a_4_2·b_5_10 + b_2_2·a_7_8 + a_2_1·b_2_22·b_3_3
  76. a_2_1·a_7_8
  77. b_6_13·b_3_4 + b_2_2·b_7_16 + b_4_7·a_5_6 + b_4_6·a_5_6 + a_4_2·b_5_10
  78. b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9 + b_4_6·a_5_6 + a_4_2·b_5_9 + a_2_1·b_7_16
  79. b_6_13·b_3_4 + b_4_7·b_5_10 + b_4_7·b_5_9 + b_2_2·b_7_17 + b_4_7·a_5_6 + b_4_6·a_5_6
       + a_4_2·b_5_10 + a_4_2·b_5_9
  80. b_2_2·b_4_7·b_3_3 + b_2_22·b_5_9 + a_4_2·b_5_9 + a_2_1·b_7_17
  81. a_8_8·a_1_0
  82. b_4_7·b_1_12·b_3_3 + b_4_6·b_4_7·b_1_1 + a_8_8·b_1_1 + b_4_7·b_1_12·a_3_2
       + b_4_6·a_5_6 + b_4_6·b_1_12·a_3_2
  83. a_5_62
  84. a_5_6·b_5_9 + a_2_1·b_4_72
  85. b_5_102 + b_5_92 + b_2_23·b_4_7 + a_2_1·b_2_22·b_4_7 + a_2_1·b_2_24
  86. a_5_6·b_5_10 + a_2_1·b_4_72 + a_2_1·b_4_6·b_4_7
  87. a_4_2·a_6_6
  88. b_5_9·b_5_10 + b_5_92 + b_2_2·b_4_6·b_4_7 + b_4_7·a_3_2·b_3_3 + b_4_6·a_3_2·b_3_3
       + b_4_6·a_6_6 + a_2_1·b_4_6·b_4_7
  89. b_5_9·b_5_10 + b_5_92 + b_2_2·b_4_6·b_4_7 + a_4_2·b_6_13 + a_2_1·b_4_72
       + a_2_1·b_4_6·b_4_7 + a_2_1·b_2_2·b_6_13
  90. a_3_2·a_7_8
  91. b_5_9·b_5_10 + b_5_92 + b_2_2·b_4_6·b_4_7 + b_3_4·a_7_8 + a_4_2·b_6_13 + a_2_1·b_4_72
       + a_2_1·b_2_22·b_4_7 + a_2_1·b_2_22·b_4_6 + a_2_1·b_2_24
  92. b_5_9·b_5_10 + b_5_92 + b_1_13·b_7_16 + b_1_15·b_5_9 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_4_7·b_1_12 + b_2_2·b_4_6·b_4_7 + b_3_3·a_7_8 + b_4_7·a_3_2·b_3_3
       + b_4_6·a_3_2·b_3_3 + b_4_6·b_1_13·a_3_2 + a_4_2·b_6_13 + a_2_1·b_4_72
       + a_2_1·b_4_6·b_4_7 + a_2_1·b_2_24
  93. b_3_3·a_7_8 + a_3_2·b_7_16 + b_1_13·a_7_8 + b_4_7·a_3_2·b_3_3 + a_2_1·b_4_6·b_4_7
       + a_2_1·b_2_22·b_4_6 + a_2_1·b_2_24
  94. b_5_9·b_5_10 + b_5_92 + b_3_4·b_7_16 + b_2_2·b_4_6·b_4_7 + b_2_22·b_6_13 + a_4_2·b_6_13
       + a_2_1·b_4_6·b_4_7 + a_2_1·b_2_22·b_4_6
  95. b_3_3·b_7_16 + b_4_7·b_1_1·b_5_9 + b_4_72·b_1_12 + b_4_6·b_1_1·b_5_9 + b_2_22·b_6_13
       + b_1_13·a_7_8 + b_4_6·a_3_2·b_3_3 + a_2_1·b_4_6·b_4_7
  96. b_5_9·b_5_10 + b_5_92 + b_2_2·b_4_6·b_4_7 + a_3_2·b_7_17 + b_4_6·a_3_2·b_3_3
       + b_4_6·b_1_13·a_3_2 + a_4_2·b_6_13 + a_2_1·b_4_72 + a_2_1·b_2_22·b_4_6
  97. b_5_9·b_5_10 + b_5_92 + b_3_4·b_7_17 + b_2_22·b_6_13 + a_4_2·b_6_13 + a_2_1·b_4_72
       + a_2_1·b_4_6·b_4_7 + a_2_1·b_2_22·b_4_7 + a_2_1·b_2_22·b_4_6
  98. b_5_9·b_5_10 + b_5_92 + b_3_3·b_7_17 + b_4_6·b_4_7·b_1_12 + b_4_62·b_1_12
       + b_2_22·b_6_13 + b_3_3·a_7_8 + b_4_6·a_3_2·b_3_3 + b_4_6·b_1_13·a_3_2 + a_4_2·b_6_13
       + a_2_1·b_4_72 + a_2_1·b_4_6·b_4_7 + a_2_1·b_2_22·b_4_6 + a_2_1·b_2_24
  99. b_5_92 + b_4_7·b_1_1·b_5_9 + b_4_72·b_1_12 + b_4_6·b_1_16 + b_2_2·b_4_72
       + c_8_22·b_1_12
  100. a_4_2·b_6_13 + b_2_2·a_8_8 + a_2_1·b_4_72 + a_2_1·b_4_6·b_4_7
  101. a_2_1·a_8_8
  102. a_1_0·b_9_27
  103. b_1_1·b_9_27 + b_1_15·b_5_9 + b_4_7·b_1_1·b_5_9 + b_4_6·b_1_16 + b_4_6·b_4_7·b_1_12
       + b_3_3·a_7_8 + b_1_13·a_7_8 + b_4_7·a_3_2·b_3_3 + b_4_6·b_1_13·a_3_2 + a_4_2·b_6_13
       + a_2_1·b_4_72 + a_2_1·b_2_22·b_4_7
  104. a_6_6·a_5_6
  105. b_4_72·b_3_4 + b_2_2·b_4_7·b_5_9 + b_6_13·a_5_6
  106. a_4_2·a_7_8
  107. b_1_1·a_3_2·b_7_16 + b_1_14·a_7_8 + a_6_6·b_5_10 + a_6_6·b_5_9 + b_4_6·a_7_8
       + b_4_6·b_4_7·a_3_2
  108. a_6_6·b_5_10 + a_6_6·b_5_9 + a_4_2·b_7_16 + a_2_1·b_4_7·b_5_9 + a_2_1·b_2_2·b_7_16
       + a_2_1·b_2_22·b_5_10
  109. b_6_13·b_5_10 + b_6_13·b_5_9 + b_4_7·b_1_12·b_5_9 + b_4_6·b_7_16 + b_4_6·b_1_12·b_5_9
       + b_4_6·b_4_7·b_3_3 + b_2_2·b_4_6·b_5_9 + a_6_6·b_5_10 + a_6_6·b_5_9 + b_4_7·a_7_8
       + b_4_62·a_3_2 + a_2_1·b_2_22·b_5_10 + a_2_1·b_2_22·b_5_9
  110. a_6_6·b_5_10 + b_4_7·a_7_8 + b_4_6·a_7_8 + a_4_2·b_7_17 + a_4_2·b_7_16
  111. b_2_2·b_4_6·b_5_9 + b_2_22·b_7_17 + b_2_22·b_7_16 + a_6_6·b_5_9 + b_4_7·a_7_8
       + b_4_6·a_7_8 + a_2_1·b_4_7·b_5_9 + a_2_1·b_2_22·b_5_10 + a_2_1·b_2_22·b_5_9
  112. a_6_6·b_5_9 + b_4_7·a_7_8 + b_4_6·a_7_8 + a_4_2·b_7_16 + a_2_1·b_2_2·b_7_17
       + a_2_1·b_2_22·b_5_10
  113. b_6_13·b_5_10 + b_6_13·b_5_9 + b_4_6·b_7_17 + b_4_62·b_3_3 + b_4_62·b_1_13
       + b_2_2·b_4_7·b_5_9 + b_2_23·b_5_9 + b_4_6·a_7_8 + a_4_2·b_7_16 + a_2_1·b_2_22·b_5_10
       + a_2_1·b_2_22·b_5_9 + a_2_1·b_2_23·b_3_3
  114. b_6_13·b_5_9 + b_4_7·b_7_16 + b_4_72·b_3_3 + b_4_6·b_1_12·b_5_9 + b_2_2·b_4_7·b_5_9
       + b_4_6·b_4_7·a_3_2 + a_2_1·b_4_7·b_5_9 + a_2_1·b_2_22·b_5_9 + a_2_1·b_2_23·b_3_3
       + b_2_2·c_8_22·b_1_1
  115. a_8_8·a_3_2
  116. a_8_8·b_3_4 + a_6_6·b_5_10 + b_4_7·a_7_8 + b_4_6·a_7_8 + a_4_2·b_7_16
  117. a_8_8·b_3_3 + a_6_6·b_5_10 + b_4_7·a_7_8 + b_4_72·a_3_2 + b_4_6·a_7_8 + b_4_62·a_3_2
       + a_4_2·b_7_16 + a_2_1·b_4_7·b_5_9 + a_2_1·b_2_22·b_5_9
  118. b_6_13·b_5_10 + b_6_13·b_5_9 + b_2_2·b_9_27 + b_2_2·b_4_6·b_5_9 + b_2_23·b_5_10
       + b_2_24·b_3_3 + a_6_6·b_5_9 + b_4_7·a_7_8 + b_4_6·a_7_8 + a_4_2·b_7_16
       + a_2_1·b_2_22·b_5_10
  119. a_6_6·b_5_9 + b_4_7·a_7_8 + b_4_6·a_7_8 + a_2_1·b_9_27 + a_2_1·b_2_23·b_3_3
  120. a_6_62
  121. a_5_6·a_7_8
  122. b_5_10·a_7_8 + b_5_9·a_7_8 + a_2_1·b_4_6·b_6_13 + a_2_1·b_2_2·b_4_72
       + a_2_1·b_2_2·b_4_6·b_4_7 + a_2_1·b_2_23·b_4_7 + a_2_1·b_2_23·b_4_6
  123. a_5_6·b_7_16 + a_2_1·b_4_7·b_6_13
  124. b_5_10·b_7_16 + b_5_9·b_7_16 + b_2_2·b_4_6·b_6_13 + b_2_2·b_4_7·a_6_6
       + a_2_1·b_4_6·b_6_13 + a_2_1·b_2_2·b_4_6·b_4_7
  125. b_5_10·b_7_17 + b_4_72·b_1_1·b_3_3 + b_4_6·b_1_1·b_7_16 + b_4_6·b_4_72
       + b_4_62·b_4_7 + b_2_2·b_4_7·b_6_13 + b_2_2·b_4_6·b_6_13 + b_5_10·a_7_8 + a_6_6·b_6_13
       + b_4_6·b_1_1·a_7_8 + b_4_6·b_4_7·b_1_1·a_3_2 + a_2_1·b_4_7·b_6_13
       + a_2_1·b_2_22·b_6_13 + a_2_1·b_2_23·b_4_7 + a_2_1·b_2_23·b_4_6
  126. a_5_6·b_7_17 + b_2_2·b_4_7·a_6_6 + a_2_1·b_2_2·b_4_6·b_4_7 + a_2_1·b_2_23·b_4_7
  127. b_5_9·b_7_17 + b_4_72·b_1_1·b_3_3 + b_4_6·b_1_1·b_7_16 + b_4_6·b_4_72 + b_4_62·b_4_7
       + b_2_2·b_4_7·b_6_13 + b_2_22·b_4_72 + b_5_10·a_7_8 + a_6_6·b_6_13 + b_4_6·b_1_1·a_7_8
       + b_4_6·b_4_7·b_1_1·a_3_2 + b_2_2·b_4_7·a_6_6 + a_2_1·b_4_7·b_6_13 + a_2_1·b_4_6·b_6_13
       + a_2_1·b_2_22·b_6_13 + a_2_1·b_2_23·b_4_6
  128. b_5_10·a_7_8 + b_4_7·b_1_1·a_7_8 + b_4_72·b_1_1·a_3_2 + b_4_6·b_1_15·a_3_2
       + b_2_2·b_4_7·a_6_6 + a_2_1·b_4_6·b_6_13 + a_2_1·b_2_2·b_4_6·b_4_7
       + a_2_1·b_2_23·b_4_7 + a_2_1·b_2_23·b_4_6 + c_8_22·b_1_1·a_3_2
  129. b_6_132 + b_4_73 + b_4_62·b_1_14 + b_4_62·b_4_7 + b_2_2·b_4_7·b_6_13
       + b_2_22·b_4_72 + b_2_24·b_4_7 + b_2_26 + b_2_2·b_4_7·a_6_6 + a_2_1·b_4_7·b_6_13
       + a_2_1·b_2_2·b_4_6·b_4_7 + a_2_1·b_2_22·b_6_13 + b_2_22·c_8_22
  130. b_5_10·b_7_16 + b_4_72·b_1_1·b_3_3 + b_4_6·b_1_1·b_7_16 + b_4_6·b_1_13·b_5_9
       + b_4_6·b_1_18 + b_4_62·b_1_14 + b_2_2·b_4_7·b_6_13 + b_2_2·b_4_6·b_6_13
       + b_5_10·a_7_8 + b_4_7·b_1_1·a_7_8 + b_4_72·b_1_1·a_3_2 + b_4_6·b_1_1·a_7_8
       + b_4_6·b_1_15·a_3_2 + b_4_6·b_4_7·b_1_1·a_3_2 + a_2_1·b_4_6·b_6_13
       + a_2_1·b_2_2·b_4_72 + a_2_1·b_2_2·b_4_6·b_4_7 + a_2_1·b_2_23·b_4_6 + a_2_1·b_2_25
       + c_8_22·b_1_1·b_3_3 + c_8_22·b_1_14
  131. a_6_6·b_6_13 + b_4_7·a_8_8 + b_4_6·b_4_7·b_1_1·a_3_2 + b_4_62·b_1_1·a_3_2
       + b_2_2·b_4_7·a_6_6 + a_2_1·b_4_7·b_6_13 + a_2_1·b_4_6·b_6_13 + a_2_1·b_2_2·b_4_6·b_4_7
       + a_2_1·b_2_22·b_6_13 + a_2_1·b_2_25 + a_2_1·b_2_2·c_8_22
  132. a_4_2·a_8_8
  133. b_4_72·b_1_1·a_3_2 + b_4_6·a_8_8 + b_4_62·b_1_1·a_3_2 + b_2_2·b_4_7·a_6_6
       + a_2_1·b_4_6·b_6_13 + a_2_1·b_2_2·b_4_72 + a_2_1·b_2_2·b_4_6·b_4_7
       + a_2_1·b_2_23·b_4_7
  134. a_3_2·b_9_27 + b_1_15·a_7_8 + b_4_7·b_1_1·a_7_8 + b_4_6·b_1_15·a_3_2
       + b_4_6·b_4_7·b_1_1·a_3_2 + a_2_1·b_4_6·b_6_13 + a_2_1·b_2_2·b_4_6·b_4_7
       + a_2_1·b_2_23·b_4_7 + a_2_1·b_2_23·b_4_6 + a_2_1·b_2_25
  135. b_3_4·b_9_27 + b_2_2·b_4_6·b_6_13 + b_2_22·b_4_6·b_4_7 + b_2_24·b_4_7 + b_2_24·b_4_6
       + b_2_26 + a_2_1·b_4_7·b_6_13 + a_2_1·b_2_23·b_4_6
  136. b_3_3·b_9_27 + b_4_7·b_1_1·b_7_16 + b_4_72·b_1_1·b_3_3 + b_4_6·b_1_1·b_7_16
       + b_4_62·b_1_14 + b_2_2·b_4_6·b_6_13 + b_2_22·b_4_6·b_4_7 + b_2_24·b_4_7
       + b_2_24·b_4_6 + b_2_26 + b_1_15·a_7_8 + b_4_7·b_1_1·a_7_8 + b_4_72·b_1_1·a_3_2
       + b_4_6·b_1_15·a_3_2 + b_4_6·b_4_7·b_1_1·a_3_2 + b_4_62·b_1_1·a_3_2
       + a_2_1·b_2_2·b_4_72 + a_2_1·b_2_2·b_4_6·b_4_7 + a_2_1·b_2_23·b_4_7 + a_2_1·b_2_25
  137. a_6_6·a_7_8
  138. a_6_6·b_7_17 + b_4_6·a_6_6·b_3_3 + b_4_6·b_4_7·b_1_12·a_3_2 + b_4_62·b_1_12·a_3_2
       + a_2_1·b_4_7·b_7_16 + a_2_1·b_2_22·b_7_17 + a_2_1·b_2_23·b_5_10
       + a_2_1·b_2_23·b_5_9 + a_2_1·b_2_24·b_3_3 + a_2_1·c_8_22·b_3_4
  139. b_6_13·b_7_16 + b_4_72·b_5_9 + b_4_73·b_1_1 + b_4_6·b_1_14·b_5_9
       + b_4_6·b_4_72·b_1_1 + b_4_62·b_4_7·b_1_1 + b_2_2·b_4_7·b_7_16 + b_2_24·b_5_9
       + b_2_25·b_3_3 + a_6_6·b_7_17 + b_4_7·b_1_12·a_7_8 + a_2_1·b_4_7·b_7_16
       + a_2_1·b_2_22·b_7_16 + a_2_1·b_2_23·b_5_9 + b_2_2·c_8_22·b_3_3
  140. b_6_13·a_7_8 + a_6_6·b_7_17 + a_6_6·b_7_16 + b_4_7·b_1_12·a_7_8 + b_4_7·a_6_6·b_3_3
       + b_4_6·a_6_6·b_3_3 + b_4_6·b_4_7·b_1_12·a_3_2 + b_4_62·b_1_12·a_3_2
       + a_2_1·b_4_7·b_7_17 + a_2_1·b_2_22·b_7_16 + a_2_1·b_2_23·b_5_10
       + a_2_1·b_2_24·b_3_3 + a_2_1·c_8_22·b_3_3
  141. a_8_8·b_5_10 + a_6_6·b_7_17 + a_6_6·b_7_16 + b_4_7·a_6_6·b_3_3 + b_4_6·a_6_6·b_3_3
       + b_4_6·b_4_7·b_1_12·a_3_2 + b_4_62·b_1_12·a_3_2 + a_2_1·b_4_7·b_7_17
       + a_2_1·b_2_2·b_4_7·b_5_9 + a_2_1·b_2_23·b_5_10 + a_2_1·b_2_23·b_5_9
  142. a_8_8·a_5_6
  143. b_4_7·b_1_12·b_7_16 + b_4_6·b_4_7·b_5_9 + b_4_6·b_4_72·b_1_1 + b_4_62·b_5_9
       + b_2_2·b_4_7·b_7_17 + b_2_2·b_4_7·b_7_16 + b_2_22·b_4_7·b_5_9 + a_8_8·b_5_9
       + b_6_13·a_7_8 + a_6_6·b_7_16 + b_4_7·b_1_12·a_7_8 + b_4_6·b_1_12·a_7_8
       + b_4_6·b_4_7·b_1_12·a_3_2 + a_2_1·b_4_7·b_7_17 + a_2_1·b_4_7·b_7_16
       + a_2_1·b_2_2·b_4_7·b_5_9 + a_2_1·b_2_23·b_5_9
  144. b_6_13·b_7_17 + b_6_13·b_7_16 + b_4_7·b_9_27 + b_4_7·b_1_12·b_7_16 + b_4_73·b_1_1
       + b_4_6·b_1_14·b_5_9 + b_4_6·b_4_7·b_5_9 + b_4_62·b_1_15 + b_4_62·b_4_7·b_1_1
       + b_4_63·b_1_1 + b_2_22·b_4_7·b_5_9 + b_2_23·b_7_17 + b_2_23·b_7_16 + b_2_24·b_5_9
       + a_6_6·b_7_17 + a_6_6·b_7_16 + b_4_7·b_1_12·a_7_8 + b_4_7·a_6_6·b_3_3
       + b_4_62·b_1_12·a_3_2 + a_2_1·b_4_7·b_7_16 + a_2_1·b_2_22·b_7_16
       + a_2_1·b_2_23·b_5_9
  145. b_4_7·b_1_12·b_7_16 + b_4_6·b_4_7·b_5_9 + b_4_6·b_4_72·b_1_1 + b_4_62·b_5_9
       + b_2_2·b_4_7·b_7_17 + b_2_2·b_4_7·b_7_16 + b_2_22·b_4_7·b_5_9 + b_6_13·a_7_8
       + a_6_6·b_7_17 + b_4_7·b_1_12·a_7_8 + b_4_7·a_6_6·b_3_3 + b_4_6·b_1_12·a_7_8
       + b_4_6·a_6_6·b_3_3 + b_4_62·b_1_12·a_3_2 + a_4_2·b_9_27 + a_2_1·b_4_7·b_7_17
       + a_2_1·b_2_23·b_5_10 + a_2_1·b_2_24·b_3_3
  146. b_4_7·b_1_12·b_7_16 + b_4_6·b_4_7·b_5_9 + b_4_6·b_4_72·b_1_1 + b_4_62·b_5_9
       + b_2_2·b_4_7·b_7_17 + b_2_2·b_4_7·b_7_16 + b_2_22·b_4_7·b_5_9 + b_6_13·a_7_8
       + a_6_6·b_7_17 + b_4_7·b_1_12·a_7_8 + b_4_7·a_6_6·b_3_3 + b_4_6·b_1_12·a_7_8
       + b_4_6·a_6_6·b_3_3 + b_4_62·b_1_12·a_3_2 + a_2_1·b_4_7·b_7_17 + a_2_1·b_4_7·b_7_16
       + a_2_1·b_2_2·b_9_27 + a_2_1·b_2_2·b_4_7·b_5_9 + a_2_1·b_2_22·b_7_17
       + a_2_1·b_2_22·b_7_16 + a_2_1·b_2_24·b_3_3
  147. b_4_7·b_1_12·b_7_16 + b_4_6·b_9_27 + b_4_6·b_1_14·b_5_9 + b_4_6·b_4_72·b_1_1
       + b_4_62·b_5_9 + b_4_62·b_1_15 + b_4_62·b_4_7·b_1_1 + b_2_2·b_4_7·b_7_16
       + b_2_23·b_7_17 + b_2_23·b_7_16 + b_2_24·b_5_10 + b_6_13·a_7_8 + a_6_6·b_7_17
       + b_4_7·a_6_6·b_3_3 + b_4_6·b_4_7·b_1_12·a_3_2 + a_2_1·b_2_22·b_7_17
       + a_2_1·b_2_22·b_7_16 + a_2_1·b_2_23·b_5_10 + a_2_1·b_2_24·b_3_3
  148. a_7_82
  149. b_7_172 + b_7_16·b_7_17 + b_4_73·b_1_12 + b_4_6·b_1_15·b_5_9
       + b_4_6·b_4_7·b_1_1·b_5_9 + b_4_6·b_4_7·b_6_13 + b_4_62·b_1_16
       + b_4_62·b_4_7·b_1_12 + b_2_2·b_4_73 + a_7_8·b_7_17 + a_7_8·b_7_16 + b_4_72·a_6_6
       + b_4_6·b_4_7·a_6_6 + b_4_62·b_1_13·a_3_2 + a_2_1·b_4_73 + a_2_1·b_4_6·b_4_72
       + a_2_1·b_2_2·b_4_7·b_6_13 + a_2_1·b_2_22·b_4_72
  150. b_7_172 + b_7_162 + b_4_72·b_1_1·b_5_9 + b_4_6·b_1_110 + 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_73 + c_8_22·b_1_16
       + b_4_7·c_8_22·b_1_12
  151. b_7_16·b_7_17 + b_4_73·b_1_12 + b_4_6·b_1_15·b_5_9 + b_4_6·b_4_7·b_1_1·b_5_9
       + b_4_6·b_4_7·b_6_13 + b_2_2·b_4_73 + b_2_22·b_4_7·b_6_13 + b_2_25·b_4_7 + b_2_27
       + a_7_8·b_7_16 + b_4_72·a_6_6 + b_4_6·a_3_2·b_7_16 + b_4_6·b_4_7·a_6_6
       + b_4_62·a_3_2·b_3_3 + b_4_62·b_1_13·a_3_2 + b_4_62·a_6_6 + a_2_1·b_4_73
       + a_2_1·b_2_2·b_4_7·b_6_13 + a_2_1·b_2_22·b_4_72 + b_2_23·c_8_22
  152. b_7_172 + b_7_16·b_7_17 + b_4_73·b_1_12 + b_4_6·b_1_15·b_5_9
       + b_4_6·b_4_7·b_1_1·b_5_9 + b_4_6·b_4_7·b_6_13 + b_4_62·b_1_16
       + b_4_62·b_4_7·b_1_12 + b_2_2·b_4_73 + a_7_8·b_7_16 + b_4_72·a_6_6
       + b_4_6·a_3_2·b_7_16 + b_4_6·b_4_7·a_6_6 + b_4_62·a_3_2·b_3_3 + b_4_62·b_1_13·a_3_2
       + b_4_62·a_6_6 + a_2_1·b_4_73 + a_2_1·b_4_6·b_4_72 + a_2_1·b_2_23·b_6_13
       + a_2_1·b_2_24·b_4_7 + a_2_1·b_2_26 + a_2_1·b_2_22·c_8_22
  153. a_7_8·b_7_16 + b_4_6·a_3_2·b_7_16 + b_4_6·b_1_13·a_7_8 + b_4_6·b_1_17·a_3_2
       + b_4_6·b_4_7·a_6_6 + b_4_62·a_3_2·b_3_3 + b_4_62·b_1_13·a_3_2 + b_4_62·a_6_6
       + a_2_1·b_4_6·b_4_72 + a_2_1·b_2_2·b_4_7·b_6_13 + a_2_1·b_2_22·b_4_72
       + a_2_1·b_2_23·b_6_13 + a_2_1·b_2_24·b_4_7 + a_2_1·b_2_26 + c_8_22·a_3_2·b_3_3
       + c_8_22·b_1_13·a_3_2
  154. b_7_172 + b_7_16·b_7_17 + b_4_73·b_1_12 + b_4_6·b_1_15·b_5_9
       + b_4_6·b_4_7·b_1_1·b_5_9 + b_4_6·b_4_7·b_6_13 + b_4_62·b_1_16
       + b_4_62·b_4_7·b_1_12 + b_2_2·b_4_73 + a_7_8·b_7_16 + b_6_13·a_8_8
       + b_4_6·a_3_2·b_7_16 + b_4_6·b_4_7·a_6_6 + b_4_62·a_6_6 + a_2_1·b_2_2·b_4_7·b_6_13
       + a_2_1·b_2_22·b_4_72 + a_2_1·b_2_22·b_4_6·b_4_7 + a_2_1·b_2_23·b_6_13
       + a_2_1·b_2_24·b_4_7 + a_2_1·b_2_24·b_4_6 + a_2_1·b_4_6·c_8_22
  155. a_6_6·a_8_8
  156. b_7_16·b_7_17 + b_7_162 + b_5_10·b_9_27 + b_4_73·b_1_12 + b_4_62·b_6_13
       + b_4_63·b_1_12 + b_2_2·b_4_6·b_4_72 + b_2_25·b_4_6 + b_4_6·a_3_2·b_7_16
       + b_4_6·b_1_13·a_7_8 + b_4_6·b_4_7·a_6_6 + b_4_62·a_3_2·b_3_3 + b_4_62·b_1_13·a_3_2
       + b_4_62·a_6_6 + b_2_2·b_4_7·a_8_8 + a_2_1·b_4_6·b_4_72 + a_2_1·b_2_22·b_4_72
       + a_2_1·b_2_22·b_4_6·b_4_7 + a_2_1·b_2_23·b_6_13 + a_2_1·b_2_24·b_4_7
       + a_2_1·b_2_24·b_4_6 + a_2_1·b_2_26 + a_2_1·b_4_6·c_8_22
  157. a_5_6·b_9_27 + b_2_2·b_4_7·a_8_8 + a_2_1·b_4_73 + a_2_1·b_2_2·b_4_7·b_6_13
       + a_2_1·b_2_22·b_4_72 + a_2_1·b_2_22·b_4_6·b_4_7 + a_2_1·b_2_24·b_4_7
  158. b_7_16·b_7_17 + b_7_162 + b_5_9·b_9_27 + b_4_73·b_1_12 + b_4_62·b_6_13
       + b_4_63·b_1_12 + b_2_2·b_4_6·b_4_72 + b_2_22·b_4_7·b_6_13 + b_2_23·b_4_72
       + b_2_23·b_4_6·b_4_7 + b_2_25·b_4_7 + b_4_6·a_3_2·b_7_16 + b_4_6·b_1_13·a_7_8
       + b_4_6·b_4_7·a_6_6 + b_4_62·a_3_2·b_3_3 + b_4_62·b_1_13·a_3_2 + b_4_62·a_6_6
       + b_2_2·b_4_7·a_8_8 + a_2_1·b_2_24·b_4_6 + a_2_1·b_4_6·c_8_22
  159. a_8_8·b_7_17 + a_8_8·b_7_16 + b_4_72·a_7_8 + b_4_73·a_3_2 + b_4_6·b_1_14·a_7_8
       + b_4_6·b_4_7·a_7_8 + b_4_6·b_4_72·a_3_2 + b_4_62·a_7_8 + b_4_62·b_1_14·a_3_2
       + b_4_63·a_3_2 + a_2_1·b_2_2·b_4_7·b_7_16 + a_2_1·b_2_22·b_4_7·b_5_9
       + a_2_1·b_2_23·b_7_17 + a_2_1·b_2_23·b_7_16 + a_2_1·b_2_24·b_5_9
  160. a_8_8·a_7_8
  161. a_8_8·b_7_16 + b_4_72·a_7_8 + b_4_73·a_3_2 + b_4_6·b_1_14·a_7_8 + b_4_6·b_4_7·a_7_8
       + b_4_62·a_7_8 + b_4_62·b_4_7·a_3_2 + a_2_1·b_4_7·b_9_27 + a_2_1·b_2_22·b_4_7·b_5_9
       + a_2_1·b_2_24·b_5_10 + a_2_1·b_2_25·b_3_3 + a_2_1·c_8_22·b_5_10 + a_2_1·c_8_22·b_5_9
       + a_2_1·b_2_2·c_8_22·b_3_3
  162. b_6_13·b_9_27 + b_4_72·b_7_17 + b_4_72·b_7_16 + b_4_73·b_3_3 + b_4_6·b_1_16·b_5_9
       + b_4_62·b_1_12·b_5_9 + b_4_62·b_1_17 + b_4_63·b_1_13 + b_2_2·b_4_72·b_5_9
       + b_2_22·b_4_7·b_7_16 + b_2_23·b_9_27 + b_2_24·b_7_16 + b_2_25·b_5_9 + b_2_26·b_3_3
       + a_8_8·b_7_16 + b_4_72·a_7_8 + b_4_6·b_4_72·a_3_2 + b_4_62·a_7_8
       + b_4_62·b_1_14·a_3_2 + b_4_63·a_3_2 + a_2_1·b_2_2·b_4_7·b_7_17
       + a_2_1·b_2_2·b_4_7·b_7_16 + a_2_1·b_2_24·b_5_10 + a_2_1·b_2_24·b_5_9
       + a_2_1·b_2_25·b_3_3 + b_2_2·c_8_22·b_5_10 + b_2_2·c_8_22·b_5_9
       + a_2_1·b_2_2·c_8_22·b_3_3
  163. a_8_8·b_7_16 + a_6_6·b_9_27 + b_4_73·a_3_2 + b_4_6·b_4_72·a_3_2
       + b_4_62·b_1_14·a_3_2 + b_4_63·a_3_2 + a_2_1·b_4_72·b_5_9
       + a_2_1·b_2_2·b_4_7·b_7_16 + a_2_1·b_2_23·b_7_16 + a_2_1·b_2_24·b_5_9
       + a_2_1·b_2_2·c_8_22·b_3_3
  164. a_8_82
  165. b_7_16·b_9_27 + b_4_6·b_1_17·b_5_9 + b_4_6·b_1_112 + b_4_6·b_4_73
       + b_4_62·b_1_1·b_7_16 + b_4_62·b_1_13·b_5_9 + b_4_62·b_1_18 + b_4_63·b_1_14
       + b_4_64 + b_2_23·b_4_7·b_6_13 + b_2_23·b_4_6·b_6_13 + b_2_24·b_4_72
       + b_2_24·b_4_6·b_4_7 + b_2_25·b_6_13 + b_2_26·b_4_6 + b_4_72·b_1_1·a_7_8
       + b_4_72·a_8_8 + b_4_6·b_1_19·a_3_2 + b_4_6·b_4_7·a_8_8 + b_4_62·b_4_7·b_1_1·a_3_2
       + b_4_63·b_1_1·a_3_2 + b_2_2·b_4_72·a_6_6 + a_2_1·b_4_6·b_4_7·b_6_13
       + a_2_1·b_2_2·b_4_73 + a_2_1·b_2_23·b_4_6·b_4_7 + a_2_1·b_2_25·b_4_6
       + c_8_22·b_1_18 + b_4_7·c_8_22·b_1_1·b_3_3 + b_4_6·c_8_22·b_1_14 + b_4_62·c_8_22
       + b_2_22·b_4_7·c_8_22 + b_2_22·b_4_6·c_8_22 + c_8_22·b_1_15·a_3_2
       + b_4_6·c_8_22·b_1_1·a_3_2 + a_2_1·b_2_23·c_8_22
  166. b_7_17·b_9_27 + b_4_73·b_1_1·b_3_3 + b_4_6·b_1_17·b_5_9 + b_4_6·b_4_7·b_1_1·b_7_16
       + b_4_6·b_4_73 + b_4_62·b_1_13·b_5_9 + b_4_62·b_1_18 + b_4_62·b_4_72
       + b_4_63·b_1_14 + b_4_63·b_4_7 + b_4_64 + b_2_2·b_4_72·b_6_13
       + b_2_23·b_4_7·b_6_13 + b_2_23·b_4_6·b_6_13 + b_2_25·b_6_13 + b_2_26·b_4_6
       + b_4_72·b_1_1·a_7_8 + b_4_72·a_8_8 + b_4_6·b_1_15·a_7_8 + b_4_6·b_1_19·a_3_2
       + b_4_6·b_4_7·b_1_1·a_7_8 + b_4_6·b_4_7·a_8_8 + b_4_62·b_4_7·b_1_1·a_3_2
       + b_4_63·b_1_1·a_3_2 + a_2_1·b_4_6·b_4_7·b_6_13 + a_2_1·b_2_23·b_4_72
       + a_2_1·b_2_25·b_4_6 + b_2_22·b_4_6·c_8_22 + c_8_22·b_1_15·a_3_2
       + b_4_7·c_8_22·b_1_1·a_3_2 + a_2_1·b_2_2·b_4_7·c_8_22
  167. a_7_8·b_9_27 + b_4_72·b_1_1·a_7_8 + b_4_6·b_1_15·a_7_8 + b_4_6·b_1_19·a_3_2
       + b_4_6·b_4_7·b_1_1·a_7_8 + b_4_6·b_4_7·a_8_8 + b_4_62·b_1_1·a_7_8
       + b_4_63·b_1_1·a_3_2 + a_2_1·b_2_23·b_4_72 + a_2_1·b_2_23·b_4_6·b_4_7
       + a_2_1·b_2_24·b_6_13 + a_2_1·b_2_25·b_4_7 + a_2_1·b_2_25·b_4_6 + a_2_1·b_2_27
       + c_8_22·b_1_15·a_3_2 + b_4_7·c_8_22·b_1_1·a_3_2 + a_2_1·b_2_2·b_4_6·c_8_22
  168. a_8_8·b_9_27 + b_4_7·a_6_6·b_7_16 + b_4_72·a_6_6·b_3_3 + b_4_6·b_1_16·a_7_8
       + b_4_6·b_4_7·b_1_12·a_7_8 + b_4_6·b_4_7·a_6_6·b_3_3 + b_4_62·b_1_16·a_3_2
       + b_4_62·a_6_6·b_3_3 + b_4_62·b_4_7·b_1_12·a_3_2 + a_2_1·b_4_72·b_7_17
       + a_2_1·b_2_2·b_4_7·b_9_27 + a_2_1·b_2_2·b_4_72·b_5_9 + a_2_1·b_2_22·b_4_7·b_7_17
       + a_2_1·b_2_22·b_4_7·b_7_16 + a_2_1·b_2_23·b_4_7·b_5_9 + a_2_1·b_2_24·b_7_17
       + a_2_1·b_2_25·b_5_10 + a_2_1·b_2_25·b_5_9 + a_2_1·b_2_2·c_8_22·b_5_10
       + a_2_1·b_2_2·c_8_22·b_5_9
  169. b_9_272 + b_4_73·b_1_1·b_5_9 + b_4_74·b_1_12 + b_4_6·b_1_114
       + b_4_62·b_1_15·b_5_9 + b_4_62·b_1_110 + b_4_63·b_6_13 + b_2_2·b_4_74
       + b_2_22·b_4_72·b_6_13 + b_2_22·b_4_6·b_4_7·b_6_13 + b_2_23·b_4_73 + b_2_29
       + b_4_62·b_4_7·a_6_6 + b_4_63·a_3_2·b_3_3 + b_4_63·a_6_6
       + a_2_1·b_2_2·b_4_6·b_4_7·b_6_13 + a_2_1·b_2_22·b_4_73
       + a_2_1·b_2_22·b_4_6·b_4_72 + a_2_1·b_2_23·b_4_6·b_6_13 + a_2_1·b_2_24·b_4_72
       + a_2_1·b_2_26·b_4_7 + a_2_1·b_2_28 + c_8_22·b_1_110 + b_4_72·c_8_22·b_1_12
       + b_2_23·b_4_7·c_8_22 + a_2_1·b_2_22·b_4_7·c_8_22 + a_2_1·b_2_24·c_8_22

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_22, a Duflot regular element of degree 8
    2. b_1_14 + b_4_7, an element of degree 4
    3. b_4_7·b_1_12 + b_2_2·b_4_7 + b_2_23, an element of degree 6
  • The Raw Filter Degree Type of that HSOP is [-1, 5, 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. a_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_2 → 0, an element of degree 4
  9. b_4_6 → 0, an element of degree 4
  10. b_4_7 → 0, an element of degree 4
  11. a_5_6 → 0, an element of degree 5
  12. b_5_9 → 0, an element of degree 5
  13. b_5_10 → 0, an element of degree 5
  14. a_6_6 → 0, an element of degree 6
  15. b_6_13 → 0, an element of degree 6
  16. a_7_8 → 0, an element of degree 7
  17. b_7_16 → 0, an element of degree 7
  18. b_7_17 → 0, an element of degree 7
  19. a_8_8 → 0, an element of degree 8
  20. c_8_22 → c_1_08, an element of degree 8
  21. b_9_27 → 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. a_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 → 0, an element of degree 3
  8. a_4_2 → 0, an element of degree 4
  9. b_4_6 → c_1_12·c_1_22 + c_1_13·c_1_2, an element of degree 4
  10. b_4_7 → c_1_24 + c_1_12·c_1_22, an element of degree 4
  11. a_5_6 → 0, an element of degree 5
  12. b_5_9 → c_1_1·c_1_24 + c_1_13·c_1_22 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  13. b_5_10 → c_1_1·c_1_24 + c_1_13·c_1_22 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  14. a_6_6 → 0, an element of degree 6
  15. b_6_13 → c_1_26 + c_1_1·c_1_25 + c_1_13·c_1_23 + c_1_15·c_1_2, an element of degree 6
  16. a_7_8 → 0, an element of degree 7
  17. b_7_16 → c_1_13·c_1_24 + c_1_15·c_1_22 + c_1_02·c_1_13·c_1_22 + c_1_02·c_1_14·c_1_2
       + c_1_02·c_1_15 + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_2 + c_1_04·c_1_13, an element of degree 7
  18. b_7_17 → c_1_13·c_1_24 + c_1_16·c_1_2, an element of degree 7
  19. a_8_8 → 0, an element of degree 8
  20. c_8_22 → c_1_28 + c_1_14·c_1_24 + c_1_16·c_1_22 + c_1_17·c_1_2
       + 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
  21. b_9_27 → c_1_1·c_1_28 + 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_18·c_1_2 + c_1_02·c_1_13·c_1_24
       + c_1_02·c_1_15·c_1_22 + c_1_02·c_1_17 + c_1_04·c_1_1·c_1_24
       + c_1_04·c_1_13·c_1_22 + c_1_04·c_1_15, 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, an element of degree 2
  5. a_3_2 → 0, an element of degree 3
  6. b_3_3 → c_1_23, an element of degree 3
  7. b_3_4 → c_1_23, an element of degree 3
  8. a_4_2 → 0, an element of degree 4
  9. b_4_6 → c_1_24 + c_1_1·c_1_23 + c_1_12·c_1_22, an element of degree 4
  10. b_4_7 → c_1_24 + c_1_12·c_1_22 + c_1_14, an element of degree 4
  11. a_5_6 → 0, an element of degree 5
  12. b_5_9 → c_1_25 + c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  13. b_5_10 → c_1_1·c_1_24 + c_1_14·c_1_2, an element of degree 5
  14. a_6_6 → 0, an element of degree 6
  15. b_6_13 → c_1_26 + c_1_1·c_1_25 + c_1_16 + c_1_02·c_1_24 + c_1_04·c_1_22, an element of degree 6
  16. a_7_8 → 0, an element of degree 7
  17. b_7_16 → c_1_27 + c_1_1·c_1_26 + c_1_16·c_1_2 + c_1_02·c_1_25 + c_1_04·c_1_23, an element of degree 7
  18. b_7_17 → c_1_13·c_1_24 + c_1_15·c_1_22 + c_1_02·c_1_25 + c_1_04·c_1_23, an element of degree 7
  19. a_8_8 → 0, an element of degree 8
  20. c_8_22 → c_1_28 + c_1_1·c_1_27 + c_1_13·c_1_25 + c_1_15·c_1_23 + c_1_18
       + c_1_02·c_1_26 + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22
       + c_1_04·c_1_12·c_1_22 + c_1_04·c_1_14 + c_1_08, an element of degree 8
  21. b_9_27 → c_1_29 + c_1_14·c_1_25 + c_1_15·c_1_24 + c_1_17·c_1_22 + c_1_18·c_1_2
       + c_1_02·c_1_27 + c_1_02·c_1_1·c_1_26 + c_1_02·c_1_12·c_1_25
       + c_1_04·c_1_25 + c_1_04·c_1_1·c_1_24 + c_1_04·c_1_12·c_1_23, 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