Cohomology of group number 37 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 4.
  • Its center has rank 2.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is of rank 4.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    t5  −  t4  +  2·t2  −  t  +  1
    (t  +  1) · (t  −  1)4 · (t2  +  1)2
  • The a-invariants are -∞,-∞,-4,-4,-4. 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 6:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. a_2_0, a nilpotent element of degree 2
  4. b_2_1, an element of degree 2
  5. b_2_2, an element of degree 2
  6. b_2_3, an element of degree 2
  7. a_3_2, a nilpotent element of degree 3
  8. a_3_4, a nilpotent element of degree 3
  9. a_3_7, a nilpotent element of degree 3
  10. b_3_3, an element of degree 3
  11. b_3_5, an element of degree 3
  12. b_3_6, an element of degree 3
  13. a_4_3, a nilpotent element of degree 4
  14. a_4_5, a nilpotent element of degree 4
  15. b_4_10, an element of degree 4
  16. c_4_11, a Duflot regular element of degree 4
  17. c_4_12, a Duflot regular element of degree 4
  18. a_5_16, a nilpotent element of degree 5
  19. b_5_17, an element of degree 5
  20. a_6_9, a nilpotent element of degree 6

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

Ring relations

There are 132 minimal relations of maximal degree 12:

  1. a_1_02
  2. a_1_12
  3. a_1_0·a_1_1
  4. a_2_0·a_1_1
  5. a_2_0·a_1_0
  6. b_2_1·a_1_0
  7. b_2_2·a_1_1
  8. b_2_2·a_1_0 + b_2_1·a_1_1
  9. b_2_3·a_1_0 + b_2_1·a_1_1
  10. a_2_02
  11. b_2_22 + b_2_1·b_2_3 + b_2_12
  12. a_2_0·b_2_1 + a_1_1·a_3_2
  13. a_1_0·a_3_2
  14. a_2_0·b_2_2 + a_1_1·a_3_4
  15. a_2_0·b_2_1 + a_1_0·a_3_4
  16. a_2_0·b_2_3 + a_2_0·b_2_2 + a_2_0·b_2_1 + a_1_1·a_3_7
  17. a_1_0·a_3_7
  18. a_1_1·b_3_3 + a_2_0·b_2_1
  19. a_1_0·b_3_3
  20. a_1_1·b_3_5 + a_2_0·b_2_2 + a_2_0·b_2_1
  21. a_1_0·b_3_5 + a_2_0·b_2_2 + a_2_0·b_2_1
  22. a_1_1·b_3_6
  23. a_1_0·b_3_6
  24. a_2_0·a_3_2
  25. b_2_2·a_3_2 + b_2_1·a_3_4
  26. b_2_3·a_3_2 + b_2_2·a_3_4 + b_2_1·a_3_2
  27. a_2_0·a_3_4
  28. b_2_3·a_3_2 + b_2_2·a_3_2 + b_2_1·a_3_7 + b_2_1·a_3_2
  29. a_2_0·a_3_7
  30. a_2_0·b_3_3
  31. b_2_2·b_3_3 + b_2_1·b_3_5 + b_2_1·b_3_3
  32. b_2_3·b_3_3 + b_2_2·b_3_5 + b_2_2·b_3_3 + b_2_1·b_3_3 + b_2_3·a_3_4 + b_2_3·a_3_2
       + b_2_2·a_3_7 + b_2_2·a_3_2 + b_2_1·a_3_2
  33. a_2_0·b_3_5
  34. b_2_3·b_3_3 + b_2_2·b_3_3 + b_2_1·b_3_6 + b_2_1·b_3_3 + b_2_3·a_3_4 + b_2_2·a_3_7
  35. b_2_3·b_3_5 + b_2_2·b_3_6 + b_2_2·b_3_3 + b_2_1·b_3_3 + b_2_2·a_3_7
  36. a_2_0·b_3_6
  37. a_4_3·a_1_1
  38. a_4_3·a_1_0
  39. a_4_5·a_1_1
  40. a_4_5·a_1_0
  41. b_4_10·a_1_1 + b_2_3·a_3_4 + b_2_3·a_3_2 + b_2_2·a_3_7 + b_2_2·a_3_2 + b_2_1·a_3_2
  42. b_4_10·a_1_0
  43. a_3_22
  44. a_3_2·a_3_4
  45. a_3_42
  46. a_3_2·a_3_7
  47. a_3_72 + b_2_3·a_1_1·a_3_7
  48. b_3_32 + b_2_13
  49. a_3_4·b_3_3 + a_3_2·b_3_5 + a_3_2·b_3_3
  50. a_3_7·b_3_3 + a_3_4·b_3_5 + a_3_4·a_3_7
  51. b_3_3·b_3_5 + b_2_12·b_2_2 + b_2_13
  52. b_3_52 + b_2_12·b_2_3
  53. a_3_7·b_3_3 + a_3_2·b_3_6 + a_3_4·a_3_7
  54. a_3_7·b_3_5 + a_3_7·b_3_3 + a_3_4·b_3_6 + a_3_4·a_3_7
  55. b_3_3·b_3_6 + b_2_12·b_2_3 + b_2_12·b_2_2 + b_2_13 + a_3_7·b_3_3 + a_3_4·a_3_7
  56. b_3_5·b_3_6 + b_2_1·b_2_2·b_2_3 + a_3_7·b_3_5
  57. b_3_62 + b_2_1·b_2_32 + b_2_12·b_2_3
  58. a_3_2·b_3_3 + b_2_1·a_4_3
  59. a_3_7·b_3_3 + a_3_4·b_3_3 + a_3_2·b_3_3 + b_2_3·a_4_3
  60. a_3_4·b_3_3 + b_2_2·a_4_3
  61. a_2_0·a_4_3
  62. a_3_7·b_3_3 + b_2_1·a_4_5 + a_3_4·a_3_7
  63. a_3_7·b_3_6 + a_3_7·b_3_5 + b_2_3·a_4_5
  64. a_3_7·b_3_5 + a_3_7·b_3_3 + b_2_2·a_4_5 + a_3_4·a_3_7
  65. a_2_0·a_4_5
  66. a_2_0·b_4_10 + a_3_4·a_3_7
  67. a_3_4·a_3_7 + a_1_1·a_5_16
  68. a_1_0·a_5_16
  69. a_1_1·b_5_17
  70. a_1_0·b_5_17
  71. a_4_3·a_3_2
  72. a_4_3·a_3_7
  73. a_4_3·a_3_4
  74. a_4_3·b_3_3 + b_2_12·a_3_2
  75. a_4_3·b_3_5 + b_2_12·a_3_4 + b_2_12·a_3_2
  76. a_4_3·b_3_6 + b_2_12·a_3_7
  77. a_4_5·a_3_2
  78. a_4_5·a_3_7
  79. a_4_5·a_3_4
  80. a_4_5·b_3_3 + b_2_12·a_3_7
  81. a_4_5·b_3_5 + b_2_1·b_2_2·a_3_7 + b_2_12·a_3_7
  82. a_4_5·b_3_6 + b_2_1·b_2_3·a_3_7 + b_2_1·b_2_2·a_3_7 + b_2_12·a_3_7
  83. b_4_10·a_3_2 + b_2_1·a_5_16 + b_2_1·b_2_2·a_3_7 + b_2_12·a_3_7 + b_2_12·a_3_4
       + b_2_12·a_3_2
  84. b_4_10·a_3_7 + b_4_10·a_3_4 + b_4_10·a_3_2 + b_2_3·a_5_16 + b_2_2·b_2_3·a_3_7
       + b_2_1·b_2_3·a_3_7 + b_2_1·b_2_2·a_3_7 + b_2_12·a_3_4 + b_2_12·a_3_2
       + b_2_3·c_4_12·a_1_1 + b_2_3·c_4_11·a_1_1 + b_2_1·c_4_12·a_1_1
  85. b_4_10·a_3_4 + b_2_32·a_3_4 + b_2_2·a_5_16 + b_2_2·b_2_3·a_3_7 + b_2_1·b_2_2·a_3_7
       + b_2_3·c_4_12·a_1_1 + b_2_3·c_4_11·a_1_1 + b_2_1·c_4_12·a_1_1
  86. a_2_0·a_5_16
  87. b_4_10·b_3_3 + b_2_1·b_5_17 + b_2_12·b_3_6 + b_2_12·b_3_5 + b_2_12·b_3_3 + b_4_10·a_3_2
       + b_2_32·a_3_4 + b_2_2·b_2_3·a_3_7 + b_2_1·b_2_3·a_3_7 + b_2_12·a_3_7 + b_2_12·a_3_4
       + b_2_12·a_3_2 + b_2_3·c_4_12·a_1_1 + b_2_3·c_4_11·a_1_1 + b_2_1·c_4_11·a_1_1
  88. b_4_10·b_3_6 + b_4_10·b_3_5 + b_2_3·b_5_17 + b_2_1·b_2_3·b_3_6 + b_2_1·b_2_2·b_3_6
       + b_2_12·b_3_6 + b_4_10·a_3_4 + b_4_10·a_3_2 + b_2_32·a_3_4 + b_2_2·b_2_3·a_3_7
       + b_2_12·a_3_7 + b_2_12·a_3_4 + b_2_12·a_3_2 + b_2_3·c_4_11·a_1_1 + b_2_1·c_4_12·a_1_1
  89. b_4_10·b_3_5 + b_4_10·b_3_3 + b_2_2·b_5_17 + b_2_1·b_2_2·b_3_6 + b_2_12·b_3_6
       + b_2_12·b_3_5 + b_2_12·b_3_3 + b_4_10·a_3_4 + b_2_1·b_2_2·a_3_7
  90. a_2_0·b_5_17
  91. a_6_9·a_1_1
  92. a_6_9·a_1_0
  93. a_4_32
  94. a_4_3·a_4_5
  95. a_4_52
  96. b_4_102 + b_2_32·b_4_10 + b_2_1·b_2_2·b_4_10 + b_2_12·b_4_10 + b_2_12·b_2_32
       + b_2_13·b_2_3 + b_2_32·a_4_5 + b_2_1·b_2_3·a_4_5 + b_2_12·a_4_5 + b_2_32·c_4_12
       + b_2_32·c_4_11 + b_2_1·b_2_3·c_4_12 + b_2_1·b_2_3·c_4_11 + b_2_12·c_4_11
  97. a_3_2·a_5_16
  98. a_3_7·a_5_16
  99. a_3_4·a_5_16 + b_2_3·a_1_1·a_5_16 + c_4_12·a_1_1·a_3_7 + c_4_11·a_1_1·a_3_7
       + c_4_11·a_1_0·a_3_4
  100. b_3_3·a_5_16 + a_4_3·b_4_10 + b_2_1·b_2_2·a_4_5 + b_2_1·b_2_2·a_4_3 + b_2_12·a_4_5
       + b_2_12·a_4_3
  101. b_3_6·a_5_16 + a_4_5·b_4_10 + b_2_2·b_2_3·a_4_5 + b_2_1·b_2_2·a_4_5 + b_2_12·a_4_5
  102. a_3_2·b_5_17 + a_4_3·b_4_10 + b_2_1·b_2_2·a_4_3 + b_2_12·a_4_5 + b_2_3·a_1_1·a_5_16
       + c_4_12·a_1_1·a_3_7 + c_4_12·a_1_0·a_3_4 + c_4_11·a_1_1·a_3_7
  103. a_3_7·b_5_17 + a_4_5·b_4_10 + b_2_1·b_2_3·a_4_5 + b_2_12·a_4_5 + c_4_12·a_1_1·a_3_7
       + c_4_11·a_1_0·a_3_4
  104. b_3_5·a_5_16 + a_3_4·b_5_17 + a_4_3·b_4_10 + b_2_1·b_2_3·a_4_5 + b_2_1·b_2_2·a_4_5
       + b_2_12·a_4_3 + b_2_3·a_1_1·a_5_16 + c_4_12·a_1_1·a_3_7 + c_4_12·a_1_1·a_3_4
       + c_4_11·a_1_1·a_3_7 + c_4_11·a_1_1·a_3_4 + c_4_11·a_1_0·a_3_4
  105. b_3_3·b_5_17 + b_2_12·b_4_10 + b_2_13·b_2_3 + b_2_14 + a_4_3·b_4_10
       + b_2_1·b_2_2·a_4_3 + b_2_12·a_4_3 + b_2_3·a_1_1·a_5_16 + c_4_12·a_1_1·a_3_7
       + c_4_12·a_1_0·a_3_4 + c_4_11·a_1_1·a_3_7
  106. b_3_5·b_5_17 + b_2_1·b_2_2·b_4_10 + b_2_12·b_4_10 + b_2_12·b_2_2·b_2_3 + b_2_13·b_2_3
       + b_2_13·b_2_2 + b_2_14 + b_3_5·a_5_16 + b_2_1·b_2_3·a_4_5 + c_4_12·a_1_1·a_3_4
       + c_4_12·a_1_0·a_3_4 + c_4_11·a_1_1·a_3_4 + c_4_11·a_1_0·a_3_4
  107. b_3_6·b_5_17 + b_2_1·b_2_3·b_4_10 + b_2_1·b_2_2·b_4_10 + b_2_12·b_4_10
       + b_2_12·b_2_32 + b_2_12·b_2_2·b_2_3 + b_2_13·b_2_2 + b_2_14 + b_2_1·b_2_3·a_4_5
       + b_2_1·b_2_2·a_4_5
  108. a_4_3·b_4_10 + b_2_1·a_6_9 + b_2_12·a_4_5 + b_2_12·a_4_3 + b_2_3·a_1_1·a_5_16
       + c_4_12·a_1_1·a_3_7 + c_4_12·a_1_0·a_3_4 + c_4_11·a_1_1·a_3_7 + c_4_11·a_1_0·a_3_4
  109. b_3_5·a_5_16 + a_4_5·b_4_10 + b_2_3·a_6_9 + b_2_3·a_1_1·a_5_16 + c_4_12·a_1_1·a_3_7
       + c_4_12·a_1_1·a_3_4 + c_4_12·a_1_0·a_3_4 + c_4_11·a_1_1·a_3_7 + c_4_11·a_1_0·a_3_4
  110. b_3_5·a_5_16 + a_4_3·b_4_10 + b_2_2·a_6_9 + b_2_1·b_2_3·a_4_5 + b_2_1·b_2_2·a_4_5
       + b_2_12·a_4_5 + b_2_12·a_4_3 + b_2_3·a_1_1·a_5_16 + c_4_12·a_1_1·a_3_7
       + c_4_12·a_1_1·a_3_4 + c_4_11·a_1_1·a_3_7 + c_4_11·a_1_0·a_3_4
  111. a_2_0·a_6_9
  112. a_4_3·a_5_16
  113. a_4_5·a_5_16
  114. b_4_10·a_5_16 + b_2_32·a_5_16 + b_2_2·b_2_3·a_5_16 + b_2_2·b_2_32·a_3_7
       + b_2_12·b_2_3·a_3_7 + b_2_13·a_3_7 + b_2_13·a_3_4 + b_2_13·a_3_2
       + b_2_3·c_4_12·a_3_7 + b_2_3·c_4_11·a_3_7 + b_2_32·c_4_12·a_1_1 + b_2_32·c_4_11·a_1_1
       + b_2_2·c_4_12·a_3_7 + b_2_2·c_4_11·a_3_7 + b_2_1·c_4_12·a_3_7 + b_2_1·c_4_11·a_3_7
       + b_2_1·c_4_11·a_3_2
  115. a_4_3·b_5_17 + b_2_12·a_5_16 + b_2_12·b_2_2·a_3_7 + b_2_13·a_3_2
  116. a_4_5·b_5_17 + b_2_1·b_2_3·a_5_16 + b_2_1·b_2_2·a_5_16 + b_2_1·b_2_2·b_2_3·a_3_7
       + b_2_12·a_5_16 + b_2_12·b_2_3·a_3_7 + b_2_12·b_2_2·a_3_7
  117. b_4_10·b_5_17 + b_2_32·b_5_17 + b_2_1·b_2_3·b_5_17 + b_2_1·b_2_32·b_3_6
       + b_2_1·b_2_2·b_5_17 + b_2_1·b_2_2·b_2_3·b_3_6 + b_2_12·b_2_3·b_3_6
       + b_2_12·b_2_2·b_3_6 + b_2_13·b_3_6 + b_2_13·b_3_5 + b_2_13·b_3_3
       + b_2_1·b_2_3·a_5_16 + b_2_1·b_2_2·a_5_16 + b_2_1·b_2_2·b_2_3·a_3_7
       + b_2_12·b_2_3·a_3_7 + b_2_13·a_3_4 + b_2_13·a_3_2 + b_2_3·c_4_12·b_3_6
       + b_2_3·c_4_11·b_3_6 + b_2_2·c_4_12·b_3_6 + b_2_2·c_4_11·b_3_6 + b_2_1·c_4_12·b_3_6
       + b_2_1·c_4_11·b_3_6 + b_2_1·c_4_11·b_3_3 + b_2_3·c_4_12·a_3_4 + b_2_32·c_4_12·a_1_1
       + b_2_2·c_4_12·a_3_7 + b_2_1·c_4_12·a_3_7 + b_2_1·c_4_11·a_3_2
  118. a_6_9·a_3_2
  119. a_6_9·a_3_7
  120. a_6_9·a_3_4
  121. a_6_9·b_3_3 + b_2_12·a_5_16 + b_2_12·b_2_2·a_3_7 + b_2_13·a_3_4
  122. a_6_9·b_3_5 + b_2_1·b_2_2·a_5_16 + b_2_12·a_5_16 + b_2_12·b_2_3·a_3_7
       + b_2_12·b_2_2·a_3_7
  123. a_6_9·b_3_6 + b_2_1·b_2_3·a_5_16 + b_2_1·b_2_2·a_5_16 + b_2_1·b_2_2·b_2_3·a_3_7
       + b_2_12·a_5_16 + b_2_12·b_2_3·a_3_7 + b_2_13·a_3_7
  124. a_5_162 + b_2_32·a_1_1·a_5_16 + b_2_3·c_4_12·a_1_1·a_3_7 + b_2_3·c_4_11·a_1_1·a_3_7
  125. b_5_172 + b_2_1·b_2_32·b_4_10 + b_2_12·b_2_2·b_4_10 + b_2_13·b_4_10 + b_2_14·b_2_3
       + b_2_15 + b_2_1·b_2_32·a_4_5 + b_2_12·b_2_3·a_4_5 + b_2_13·a_4_5
       + b_2_1·b_2_32·c_4_12 + b_2_1·b_2_32·c_4_11 + b_2_12·b_2_3·c_4_12
       + b_2_12·b_2_3·c_4_11 + b_2_13·c_4_11
  126. a_4_3·a_6_9
  127. a_5_16·b_5_17 + b_2_32·a_6_9 + b_2_2·b_2_3·a_6_9 + b_2_1·b_2_3·a_6_9
       + b_2_1·b_2_32·a_4_5 + b_2_12·a_6_9 + b_2_12·b_2_2·a_4_5 + b_2_13·a_4_5
       + b_2_13·a_4_3 + b_2_32·a_1_1·a_5_16 + b_2_3·a_4_5·c_4_12 + b_2_3·a_4_5·c_4_11
       + b_2_2·a_4_5·c_4_12 + b_2_2·a_4_5·c_4_11 + b_2_1·a_4_5·c_4_12 + b_2_1·a_4_5·c_4_11
       + b_2_1·a_4_3·c_4_11 + c_4_12·a_1_1·a_5_16 + b_2_3·c_4_12·a_1_1·a_3_7
       + b_2_3·c_4_11·a_1_1·a_3_7
  128. a_4_5·a_6_9
  129. b_4_10·a_6_9 + b_2_32·a_6_9 + b_2_1·b_2_3·a_6_9 + b_2_1·b_2_32·a_4_5 + b_2_12·a_6_9
       + b_2_12·b_2_3·a_4_5 + b_2_13·a_4_5 + b_2_13·a_4_3 + b_2_3·a_4_5·c_4_12
       + b_2_3·a_4_5·c_4_11 + b_2_2·a_4_5·c_4_12 + b_2_2·a_4_5·c_4_11 + b_2_1·a_4_5·c_4_12
       + b_2_1·a_4_5·c_4_11 + b_2_1·a_4_3·c_4_11 + c_4_12·a_1_1·a_5_16 + c_4_11·a_1_1·a_5_16
  130. a_6_9·b_5_17 + b_2_1·b_2_32·a_5_16 + b_2_1·b_2_2·b_2_32·a_3_7
       + b_2_12·b_2_32·a_3_7 + b_2_12·b_2_2·b_2_3·a_3_7 + b_2_14·a_3_7 + b_2_14·a_3_2
       + b_2_1·b_2_3·c_4_12·a_3_7 + b_2_1·b_2_3·c_4_11·a_3_7 + b_2_1·b_2_2·c_4_12·a_3_7
       + b_2_1·b_2_2·c_4_11·a_3_7 + b_2_12·c_4_12·a_3_7 + b_2_12·c_4_11·a_3_7
       + b_2_12·c_4_11·a_3_2
  131. a_6_9·a_5_16
  132. a_6_92

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 12.
  • 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_4_11, a Duflot regular element of degree 4
    2. c_4_12, a Duflot regular element of degree 4
    3. b_2_3 + b_2_2, an element of degree 2
    4. b_3_6, an element of degree 3
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 4, 6, 9].
  • 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 Back to groups of order 128

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 2

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. a_2_0 → 0, an element of degree 2
  4. b_2_1 → 0, an element of degree 2
  5. b_2_2 → 0, an element of degree 2
  6. b_2_3 → 0, an element of degree 2
  7. a_3_2 → 0, an element of degree 3
  8. a_3_4 → 0, an element of degree 3
  9. a_3_7 → 0, an element of degree 3
  10. b_3_3 → 0, an element of degree 3
  11. b_3_5 → 0, an element of degree 3
  12. b_3_6 → 0, an element of degree 3
  13. a_4_3 → 0, an element of degree 4
  14. a_4_5 → 0, an element of degree 4
  15. b_4_10 → 0, an element of degree 4
  16. c_4_11 → c_1_14, an element of degree 4
  17. c_4_12 → c_1_14 + c_1_04, an element of degree 4
  18. a_5_16 → 0, an element of degree 5
  19. b_5_17 → 0, an element of degree 5
  20. a_6_9 → 0, an element of degree 6

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

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. a_2_0 → 0, an element of degree 2
  4. b_2_1 → c_1_22, an element of degree 2
  5. b_2_2 → c_1_2·c_1_3 + c_1_22, an element of degree 2
  6. b_2_3 → c_1_32, an element of degree 2
  7. a_3_2 → 0, an element of degree 3
  8. a_3_4 → 0, an element of degree 3
  9. a_3_7 → 0, an element of degree 3
  10. b_3_3 → c_1_23, an element of degree 3
  11. b_3_5 → c_1_22·c_1_3, an element of degree 3
  12. b_3_6 → c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  13. a_4_3 → 0, an element of degree 4
  14. a_4_5 → 0, an element of degree 4
  15. b_4_10 → c_1_1·c_1_23 + c_1_12·c_1_22 + c_1_02·c_1_32 + c_1_02·c_1_2·c_1_3, an element of degree 4
  16. c_4_11 → c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3
       + c_1_12·c_1_22 + c_1_14, an element of degree 4
  17. c_4_12 → c_1_24 + c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3 + c_1_1·c_1_23
       + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3 + c_1_14 + c_1_02·c_1_32
       + c_1_02·c_1_2·c_1_3 + c_1_02·c_1_22 + c_1_04, an element of degree 4
  18. a_5_16 → 0, an element of degree 5
  19. b_5_17 → c_1_23·c_1_32 + c_1_25 + c_1_1·c_1_24 + c_1_12·c_1_23 + c_1_02·c_1_2·c_1_32
       + c_1_02·c_1_22·c_1_3, an element of degree 5
  20. a_6_9 → 0, an element of degree 6

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