Cohomology of group number 970 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 3 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) · (t5  +  t4  −  t2  +  t  +  1)
    (t  +  1) · (t  −  1)3 · (t2  +  1) · (t4  +  1)
  • The a-invariants are -∞,-6,-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 14 minimal generators of maximal degree 9:

  1. a_1_2, a nilpotent element of degree 1
  2. b_1_0, an element of degree 1
  3. b_1_1, an element of degree 1
  4. b_3_3, an element of degree 3
  5. b_3_4, an element of degree 3
  6. b_4_6, an element of degree 4
  7. b_5_7, an element of degree 5
  8. b_5_8, an element of degree 5
  9. b_5_9, an element of degree 5
  10. b_6_12, an element of degree 6
  11. b_7_13, an element of degree 7
  12. b_7_15, an element of degree 7
  13. c_8_19, a Duflot regular element of degree 8
  14. b_9_24, 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 65 minimal relations of maximal degree 18:

  1. a_1_2·b_1_0
  2. b_1_0·b_1_1 + a_1_22
  3. a_1_22·b_1_1
  4. b_1_1·b_3_3
  5. a_1_2·b_3_3
  6. a_1_2·b_3_4
  7. b_1_12·b_3_4
  8. b_4_6·a_1_2
  9. b_3_32 + b_1_03·b_3_3 + b_4_6·b_1_02
  10. b_3_42 + b_3_3·b_3_4 + b_1_0·b_5_7
  11. a_1_2·b_5_7
  12. b_3_32 + b_1_0·b_5_8
  13. b_1_1·b_5_7 + a_1_2·b_5_8
  14. b_3_42 + b_3_32 + b_1_0·b_5_9
  15. b_1_1·b_5_7 + a_1_2·b_5_9
  16. b_1_12·b_5_9 + b_1_12·b_5_8 + b_4_6·b_1_13
  17. b_1_04·b_3_3 + b_6_12·b_1_0 + b_4_6·b_3_3
  18. b_6_12·a_1_2
  19. b_3_4·b_5_8 + b_3_3·b_5_9 + b_3_3·b_5_8 + b_3_3·b_5_7 + b_4_6·b_1_1·b_3_4
  20. b_3_4·b_5_9 + b_3_4·b_5_7 + b_3_3·b_5_7
  21. b_3_4·b_5_8 + b_3_3·b_5_8 + b_1_03·b_5_9 + b_1_03·b_5_7 + b_4_6·b_1_1·b_3_4
       + b_4_6·b_1_0·b_3_4 + b_4_6·b_1_0·b_3_3
  22. b_3_3·b_5_8 + b_6_12·b_1_02 + b_4_6·b_1_04
  23. b_1_1·b_7_13
  24. b_3_4·b_5_8 + b_3_3·b_5_7 + b_1_0·b_7_13 + b_1_03·b_5_7 + b_4_6·b_1_1·b_3_4
       + b_4_6·b_1_0·b_3_4 + b_4_6·b_1_0·b_3_3
  25. a_1_2·b_7_13
  26. b_3_4·b_5_7 + b_3_3·b_5_8 + b_1_0·b_7_15 + b_1_03·b_5_7 + b_4_6·b_1_0·b_3_3
  27. a_1_2·b_7_15 + a_1_2·b_1_12·b_5_8
  28. b_1_04·b_5_9 + b_1_04·b_5_7 + b_6_12·b_3_4 + b_6_12·b_3_3 + b_4_6·b_5_9 + b_4_6·b_5_8
       + b_4_6·b_5_7 + b_4_6·b_1_02·b_3_3 + b_4_62·b_1_1 + b_4_62·b_1_0
  29. b_6_12·b_3_3 + b_6_12·b_1_03 + b_4_6·b_1_05 + b_4_62·b_1_0
  30. b_1_12·b_7_15 + b_1_14·b_5_8 + b_6_12·b_1_13 + b_4_6·b_5_8 + b_4_6·b_1_15
       + b_4_6·b_1_02·b_3_3 + b_4_62·b_1_1 + b_4_62·b_1_0 + a_1_2·b_1_13·b_5_8
  31. b_5_92 + b_5_8·b_5_9 + b_5_72 + b_4_6·b_1_1·b_5_9
  32. b_5_8·b_5_9 + b_5_82 + b_5_7·b_5_8 + b_6_12·b_1_0·b_3_4 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_03·b_3_4 + b_4_62·b_1_12
  33. b_5_8·b_5_9 + b_5_82 + b_5_7·b_5_8 + b_3_3·b_7_13 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_0·b_5_9 + b_4_62·b_1_12
  34. b_5_8·b_5_9 + b_5_82 + b_1_03·b_7_13 + b_1_05·b_5_7 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_0·b_5_9 + b_4_6·b_1_03·b_3_4 + b_4_62·b_1_12 + b_4_62·b_1_02
  35. b_5_7·b_5_9 + b_5_72 + b_3_3·b_7_15 + b_6_12·b_1_04 + b_4_6·b_1_0·b_5_7
       + b_4_6·b_1_06
  36. b_5_7·b_5_8 + b_5_72 + b_3_4·b_7_15 + b_3_4·b_7_13 + b_4_6·b_1_0·b_5_9
       + b_4_6·b_1_03·b_3_3 + b_4_62·b_1_02
  37. b_5_8·b_5_9 + b_5_82 + b_5_7·b_5_9 + b_5_7·b_5_8 + b_5_72 + b_3_4·b_7_13
       + b_1_03·b_7_15 + b_1_05·b_5_7 + b_6_12·b_1_04 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_0·b_5_7 + b_4_6·b_1_03·b_3_3 + b_4_6·b_1_06 + b_4_62·b_1_12
  38. b_5_72 + b_1_05·b_5_7 + b_6_12·b_1_04 + b_4_6·b_1_03·b_3_4 + b_4_6·b_1_03·b_3_3
       + c_8_19·b_1_02
  39. b_5_82 + b_6_12·b_1_04 + b_4_6·b_1_16 + b_4_6·b_1_03·b_3_3 + b_4_6·b_1_06
       + b_4_62·b_1_12 + b_4_62·b_1_02 + a_1_2·b_1_14·b_5_8 + c_8_19·a_1_22
  40. b_5_8·b_5_9 + b_3_4·b_7_13 + b_1_0·b_9_24 + b_1_05·b_5_7 + b_4_6·b_1_1·b_5_9
       + b_4_6·b_1_16 + b_4_6·b_1_0·b_5_9 + b_4_6·b_1_0·b_5_7 + b_4_6·b_1_03·b_3_4
       + b_4_6·b_1_06 + a_1_2·b_1_14·b_5_8
  41. a_1_2·b_9_24 + c_8_19·a_1_2·b_1_1
  42. b_6_12·b_5_9 + b_6_12·b_5_8 + b_6_12·b_5_7 + b_6_12·b_1_02·b_3_4 + b_4_6·b_1_04·b_3_4
       + b_4_6·b_6_12·b_1_1 + b_4_62·b_3_4
  43. b_1_04·b_7_13 + b_1_06·b_5_7 + b_6_12·b_5_9 + b_6_12·b_5_8 + b_4_6·b_7_13
       + b_4_6·b_1_02·b_5_7 + b_4_6·b_1_04·b_3_4 + b_4_6·b_6_12·b_1_1 + b_4_6·b_6_12·b_1_0
       + b_4_62·b_3_4
  44. b_1_12·b_9_24 + b_6_12·b_5_8 + b_6_12·b_1_05 + b_4_6·b_1_17 + b_4_6·b_1_07
       + b_4_6·b_6_12·b_1_1 + b_4_6·b_6_12·b_1_0 + b_4_62·b_1_13 + b_4_62·b_1_03
       + c_8_19·b_1_13
  45. b_6_12·b_1_06 + b_6_122 + b_4_6·b_1_08 + b_4_6·b_6_12·b_1_02
       + b_4_62·b_1_1·b_3_4 + b_4_63
  46. b_5_8·b_7_13 + b_6_12·b_1_03·b_3_4 + b_4_6·b_1_0·b_7_13 + b_4_6·b_1_03·b_5_9
       + b_4_6·b_1_05·b_3_4
  47. b_5_9·b_7_13 + b_5_7·b_7_13 + b_6_12·b_1_0·b_5_7 + b_6_12·b_1_06 + b_6_122
       + b_4_6·b_1_0·b_7_15 + b_4_6·b_1_03·b_5_9 + b_4_6·b_1_03·b_5_7 + b_4_6·b_1_08
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_0·b_3_4 + b_4_62·b_1_04 + b_4_63
  48. b_5_9·b_7_15 + b_5_7·b_7_15 + b_5_7·b_7_13 + b_1_07·b_5_7 + b_6_12·b_1_1·b_5_8
       + b_6_12·b_1_0·b_5_7 + b_6_12·b_1_03·b_3_4 + b_4_6·b_1_18 + b_4_6·b_1_03·b_5_7
       + b_4_6·b_1_08 + b_4_6·b_6_12·b_1_12 + b_4_62·b_1_14 + b_4_62·b_1_04
       + a_1_2·b_1_16·b_5_8 + c_8_19·b_1_04
  49. b_5_9·b_7_15 + b_5_9·b_7_13 + b_5_8·b_7_15 + b_5_8·b_7_13 + b_5_7·b_7_15 + b_5_7·b_7_13
       + b_6_122 + b_4_6·b_1_1·b_7_15 + b_4_6·b_1_03·b_5_7 + b_4_62·b_1_1·b_3_4
       + b_4_62·b_1_0·b_3_4 + b_4_62·b_1_0·b_3_3 + b_4_63 + c_8_19·b_1_0·b_3_3
  50. b_5_9·b_7_15 + b_5_8·b_7_13 + b_5_7·b_7_13 + b_1_05·b_7_15 + b_1_07·b_5_7
       + b_6_12·b_1_1·b_5_8 + b_6_12·b_1_03·b_3_4 + b_6_12·b_1_06 + b_6_122
       + b_4_6·b_1_18 + b_4_6·b_1_03·b_5_7 + b_4_6·b_1_08 + b_4_6·b_6_12·b_1_12
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14 + b_4_63 + a_1_2·b_1_16·b_5_8
       + c_8_19·b_1_0·b_3_4
  51. b_5_9·b_7_13 + b_5_7·b_7_13 + b_3_3·b_9_24 + b_6_12·b_1_06 + b_4_6·b_1_03·b_5_9
       + b_4_6·b_1_08 + b_4_62·b_1_0·b_3_3 + b_4_62·b_1_04
  52. b_5_9·b_7_13 + b_5_8·b_7_15 + b_5_8·b_7_13 + b_3_4·b_9_24 + b_1_05·b_7_15 + b_1_07·b_5_7
       + b_6_12·b_1_1·b_5_8 + b_6_12·b_1_06 + b_6_122 + b_4_6·b_1_1·b_7_15 + b_4_6·b_1_18
       + b_4_6·b_1_03·b_5_9 + b_4_6·b_1_05·b_3_4 + b_4_6·b_1_08 + b_4_6·b_6_12·b_1_12
       + b_4_62·b_1_1·b_3_4 + b_4_62·b_1_14 + b_4_62·b_1_0·b_3_3 + b_4_63
       + a_1_2·b_1_16·b_5_8 + c_8_19·b_1_1·b_3_4
  53. b_5_9·b_7_13 + b_5_8·b_7_15 + b_5_8·b_7_13 + b_5_7·b_7_13 + b_1_03·b_9_24
       + b_1_05·b_7_15 + b_6_12·b_1_1·b_5_8 + b_6_12·b_1_03·b_3_4 + b_6_12·b_1_06
       + b_4_6·b_1_1·b_7_15 + b_4_6·b_1_18 + b_4_6·b_1_03·b_5_7 + b_4_6·b_6_12·b_1_12
       + b_4_62·b_1_14 + b_4_62·b_1_0·b_3_4 + b_4_62·b_1_04 + a_1_2·b_1_16·b_5_8
  54. b_6_12·b_7_13 + b_6_12·b_1_04·b_3_4 + b_4_6·b_1_04·b_5_7 + b_4_6·b_1_06·b_3_4
       + b_4_6·b_6_12·b_1_03 + b_4_62·b_5_7 + b_4_62·b_1_02·b_3_4 + b_4_62·b_1_05
       + b_4_63·b_1_0
  55. b_1_04·b_9_24 + b_1_06·b_7_15 + b_6_12·b_7_15 + b_6_12·b_1_12·b_5_8
       + b_6_12·b_1_02·b_5_7 + b_6_122·b_1_0 + b_4_6·b_9_24 + b_4_6·b_1_02·b_7_15
       + b_4_6·b_1_04·b_5_7 + b_4_6·b_1_06·b_3_4 + b_4_6·b_1_09 + b_4_6·b_6_12·b_3_4
       + b_4_6·b_6_12·b_1_13 + b_4_6·b_6_12·b_1_03 + b_4_62·b_5_7 + b_4_62·b_1_15
       + b_4_62·b_1_02·b_3_4 + b_4_63·b_1_0 + b_4_6·c_8_19·b_1_1
  56. b_7_132 + b_1_09·b_5_7 + b_6_12·b_1_05·b_3_4 + b_4_6·b_1_010
       + b_4_6·b_6_12·b_1_0·b_3_4 + b_4_6·b_6_12·b_1_04 + b_4_62·b_1_0·b_5_9
       + b_4_62·b_1_0·b_5_7 + b_4_62·b_1_03·b_3_4 + b_4_62·b_1_03·b_3_3
       + c_8_19·b_1_03·b_3_3 + c_8_19·b_1_06 + b_4_6·c_8_19·b_1_02
  57. b_7_13·b_7_15 + b_7_132 + b_1_07·b_7_15 + b_1_09·b_5_7 + b_6_12·b_1_0·b_7_15
       + b_6_12·b_1_03·b_5_7 + b_6_122·b_1_02 + b_4_6·b_1_03·b_7_15
       + b_4_6·b_1_03·b_7_13 + b_4_6·b_1_05·b_5_7 + b_4_6·b_1_07·b_3_4
       + b_4_6·b_6_12·b_1_04 + b_4_62·b_1_06 + c_8_19·b_1_0·b_5_9 + c_8_19·b_1_0·b_5_7
       + c_8_19·b_1_03·b_3_4
  58. b_7_152 + b_7_132 + b_5_8·b_9_24 + b_1_09·b_5_7 + b_6_12·b_1_0·b_7_15
       + b_6_12·b_1_03·b_5_7 + b_6_122·b_1_02 + b_4_6·b_1_1·b_9_24 + b_4_6·b_1_15·b_5_8
       + b_4_6·b_1_110 + b_4_6·b_1_03·b_7_15 + b_4_6·b_1_07·b_3_4 + b_4_6·b_1_010
       + b_4_6·b_6_12·b_1_14 + b_4_6·b_6_12·b_1_0·b_3_4 + b_4_62·b_1_1·b_5_8
       + b_4_62·b_1_16 + b_4_62·b_1_0·b_5_7 + b_4_63·b_1_12 + a_1_2·b_1_18·b_5_8
       + c_8_19·b_1_1·b_5_8 + c_8_19·b_1_0·b_5_9 + c_8_19·b_1_06 + b_4_6·c_8_19·b_1_12
  59. b_7_152 + b_7_132 + b_1_09·b_5_7 + b_6_12·b_1_0·b_7_15 + b_4_6·b_1_110
       + b_4_6·b_1_0·b_9_24 + b_4_6·b_1_05·b_5_7 + b_4_6·b_1_07·b_3_4 + b_4_6·b_1_010
       + b_4_6·b_6_12·b_1_0·b_3_4 + b_4_62·b_1_0·b_5_7 + b_4_62·b_1_03·b_3_4
       + b_4_62·b_1_03·b_3_3 + b_4_63·b_1_02 + a_1_2·b_1_18·b_5_8 + c_8_19·b_1_0·b_5_9
       + c_8_19·b_1_06
  60. b_7_13·b_7_15 + b_5_9·b_9_24 + b_6_12·b_1_0·b_7_15 + b_6_12·b_1_03·b_5_7
       + b_4_6·b_1_15·b_5_8 + b_4_6·b_1_05·b_5_7 + b_4_6·b_6_12·b_1_14
       + b_4_6·b_6_12·b_1_04 + b_4_62·b_1_1·b_5_8 + b_4_62·b_1_16
       + b_4_62·b_1_03·b_3_4 + b_4_62·b_1_06 + b_4_63·b_1_12 + c_8_19·b_1_1·b_5_9
  61. b_7_13·b_7_15 + b_7_132 + b_5_7·b_9_24 + b_1_09·b_5_7 + b_6_12·b_1_03·b_5_7
       + b_4_6·b_1_05·b_5_7 + b_4_6·b_1_07·b_3_4 + b_4_6·b_1_010
       + b_4_6·b_6_12·b_1_0·b_3_4 + b_4_6·b_6_12·b_1_04 + b_4_62·b_1_0·b_5_9
       + b_4_62·b_1_0·b_5_7 + b_4_62·b_1_06 + c_8_19·b_1_03·b_3_3 + c_8_19·b_1_06
       + c_8_19·a_1_2·b_5_8
  62. b_6_12·b_9_24 + b_6_12·b_1_04·b_5_7 + b_6_122·b_1_03 + b_4_6·b_1_04·b_7_15
       + b_4_6·b_1_06·b_5_7 + b_4_6·b_6_12·b_5_7 + b_4_6·b_6_12·b_1_15
       + b_4_6·b_6_12·b_1_05 + b_4_62·b_7_15 + b_4_62·b_1_12·b_5_8
       + b_4_62·b_1_02·b_5_7 + b_4_62·b_1_04·b_3_4 + b_4_62·b_1_07 + b_4_63·b_3_4
       + b_4_63·b_1_13 + b_4_63·b_1_03 + b_6_12·c_8_19·b_1_1
  63. b_7_15·b_9_24 + b_6_12·b_1_05·b_5_7 + b_6_122·b_1_0·b_3_4 + b_4_6·b_1_17·b_5_8
       + b_4_6·b_6_12·b_1_0·b_5_7 + b_4_6·b_6_122 + b_4_62·b_1_18 + b_4_62·b_1_0·b_7_15
       + b_4_62·b_1_0·b_7_13 + b_4_62·b_1_03·b_5_7 + b_4_62·b_1_05·b_3_4
       + b_4_62·b_1_08 + b_4_63·b_1_1·b_3_4 + b_4_63·b_1_0·b_3_4 + b_4_63·b_1_04
       + b_4_64 + c_8_19·b_1_1·b_7_15 + c_8_19·b_1_0·b_7_13 + b_6_12·c_8_19·b_1_02
       + b_4_6·c_8_19·b_1_0·b_3_3
  64. b_7_13·b_9_24 + b_1_09·b_7_15 + b_6_12·b_1_05·b_5_7 + b_6_122·b_1_0·b_3_4
       + b_6_122·b_1_04 + b_4_6·b_1_03·b_9_24 + b_4_6·b_1_05·b_7_15 + b_4_6·b_1_012
       + b_4_6·b_6_12·b_1_03·b_3_4 + b_4_62·b_1_0·b_7_13 + b_4_62·b_1_03·b_5_9
       + b_4_62·b_1_05·b_3_4 + b_4_62·b_1_08 + b_4_63·b_1_0·b_3_3 + b_4_63·b_1_04
       + c_8_19·b_1_03·b_5_9 + c_8_19·b_1_03·b_5_7 + c_8_19·b_1_05·b_3_4 + c_8_19·b_1_08
       + b_4_6·c_8_19·b_1_0·b_3_4 + b_4_6·c_8_19·b_1_0·b_3_3 + b_4_6·c_8_19·b_1_04
  65. b_9_242 + b_6_122·b_1_0·b_5_7 + b_4_6·b_1_09·b_5_7 + b_4_6·b_6_12·b_1_03·b_5_7
       + b_4_6·b_6_12·b_1_05·b_3_4 + b_4_6·b_6_122·b_1_02 + b_4_62·b_1_110
       + b_4_62·b_1_03·b_7_15 + b_4_62·b_1_010 + b_4_62·b_6_12·b_1_0·b_3_4
       + b_4_62·b_6_12·b_1_04 + b_4_63·b_1_03·b_3_4 + b_4_64·b_1_02
       + c_8_19·b_1_03·b_7_13 + b_6_12·c_8_19·b_1_0·b_3_4 + b_6_12·c_8_19·b_1_04
       + b_4_6·c_8_19·b_1_0·b_5_7 + b_4_6·c_8_19·b_1_03·b_3_4 + b_4_6·c_8_19·b_1_06
       + b_4_62·c_8_19·b_1_02 + c_8_192·b_1_12

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_14 + b_1_0·b_3_3 + b_1_04 + b_4_6, an element of degree 4
    3. b_1_03·b_3_3 + b_4_6·b_1_12 + b_4_6·b_1_02, an element of degree 6
  • The Raw Filter Degree Type of that HSOP is [-1, 2, 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_2 → 0, an element of degree 1
  2. b_1_0 → 0, an element of degree 1
  3. b_1_1 → 0, an element of degree 1
  4. b_3_3 → 0, an element of degree 3
  5. b_3_4 → 0, an element of degree 3
  6. b_4_6 → 0, an element of degree 4
  7. b_5_7 → 0, an element of degree 5
  8. b_5_8 → 0, an element of degree 5
  9. b_5_9 → 0, an element of degree 5
  10. b_6_12 → 0, an element of degree 6
  11. b_7_13 → 0, an element of degree 7
  12. b_7_15 → 0, an element of degree 7
  13. c_8_19 → c_1_08, an element of degree 8
  14. b_9_24 → 0, an element of degree 9

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

  1. a_1_2 → 0, an element of degree 1
  2. b_1_0 → c_1_1, an element of degree 1
  3. b_1_1 → 0, an element of degree 1
  4. b_3_3 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  5. b_3_4 → c_1_0·c_1_12 + c_1_02·c_1_1, an element of degree 3
  6. b_4_6 → c_1_24 + c_1_13·c_1_2, an element of degree 4
  7. b_5_7 → 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 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  8. b_5_8 → c_1_1·c_1_24 + c_1_13·c_1_22, an element of degree 5
  9. 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
  10. b_6_12 → 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
  11. b_7_13 → 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_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_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
  12. b_7_15 → c_1_13·c_1_24 + 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_02·c_1_15 + c_1_03·c_1_14 + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_2
       + c_1_05·c_1_12 + c_1_06·c_1_1, an element of degree 7
  13. c_8_19 → 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_15·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_08, an element of degree 8
  14. b_9_24 → 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_14·c_1_24 + c_1_0·c_1_16·c_1_22 + 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_03·c_1_14·c_1_22
       + c_1_03·c_1_15·c_1_2 + c_1_03·c_1_16 + c_1_04·c_1_13·c_1_22
       + c_1_04·c_1_14·c_1_2 + 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_2 → 0, an element of degree 1
  2. b_1_0 → 0, an element of degree 1
  3. b_1_1 → c_1_1, an element of degree 1
  4. b_3_3 → 0, an element of degree 3
  5. b_3_4 → 0, an element of degree 3
  6. b_4_6 → c_1_24 + c_1_12·c_1_22, an element of degree 4
  7. b_5_7 → 0, an element of degree 5
  8. b_5_8 → c_1_1·c_1_24 + c_1_14·c_1_2, an element of degree 5
  9. b_5_9 → c_1_13·c_1_22 + c_1_14·c_1_2, an element of degree 5
  10. b_6_12 → c_1_26 + c_1_1·c_1_25 + c_1_12·c_1_24 + c_1_13·c_1_23, an element of degree 6
  11. b_7_13 → 0, an element of degree 7
  12. b_7_15 → c_1_15·c_1_22 + c_1_16·c_1_2, an element of degree 7
  13. c_8_19 → c_1_14·c_1_24 + c_1_16·c_1_22 + 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
  14. b_9_24 → c_1_02·c_1_13·c_1_24 + 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 + c_1_04·c_1_15 + c_1_08·c_1_1, 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