Cohomology of group number 195 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 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
    t2  −  t  +  1
    (t  −  1)4 · (t2  +  1)
  • 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 14 minimal generators of maximal degree 5:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. b_1_2, an element of degree 1
  4. a_2_4, a nilpotent element of degree 2
  5. b_2_5, an element of degree 2
  6. a_3_7, a nilpotent element of degree 3
  7. a_3_6, a nilpotent element of degree 3
  8. b_3_8, an element of degree 3
  9. b_3_10, an element of degree 3
  10. b_4_16, an element of degree 4
  11. c_4_17, a Duflot regular element of degree 4
  12. c_4_18, a Duflot regular element of degree 4
  13. a_5_20, a nilpotent element of degree 5
  14. b_5_29, an element of degree 5

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

Ring relations

There are 53 minimal relations of maximal degree 10:

  1. a_1_02
  2. a_1_0·a_1_1
  3. a_1_0·b_1_22
  4. a_2_4·a_1_1 + a_1_13
  5. a_2_4·a_1_0 + a_1_13
  6. b_2_5·a_1_0 + a_1_13
  7. b_2_5·a_1_12 + a_2_42 + a_1_13·b_1_2
  8. a_1_1·a_3_7 + a_1_12·b_1_22
  9. a_1_0·a_3_7
  10. a_1_1·a_3_6
  11. a_1_0·a_3_6
  12. a_1_0·b_3_8
  13. a_1_0·b_3_10 + a_1_13·b_1_2
  14. b_1_22·a_3_6 + b_2_5·a_3_7 + b_2_5·a_1_1·b_1_22 + a_2_4·a_3_7
  15. a_1_12·b_3_8 + a_2_4·a_3_7
  16. b_2_5·a_3_7 + b_2_5·a_1_1·b_1_22 + a_2_4·b_3_8
  17. a_1_12·b_3_10 + a_2_4·a_3_6 + a_2_42·b_1_2
  18. b_2_5·a_3_6 + a_2_4·b_3_10 + a_2_4·b_2_5·b_1_2 + a_2_4·a_3_6
  19. b_1_22·b_3_10 + b_2_5·b_3_8 + b_2_5·b_1_23 + a_1_1·b_1_2·b_3_10 + a_1_1·b_1_2·b_3_8
       + b_4_16·a_1_1 + b_2_5·a_1_1·b_1_22 + b_2_52·a_1_1 + a_2_4·a_3_7 + a_2_42·b_1_2
  20. b_4_16·a_1_0
  21. a_3_72
  22. a_3_7·a_3_6 + a_2_42·b_1_22
  23. a_3_62 + a_2_42·b_2_5
  24. a_3_7·b_3_8 + a_1_1·b_1_22·b_3_8 + a_2_4·b_1_24
  25. a_3_6·b_3_8 + a_2_4·b_2_5·b_1_22 + a_2_42·b_1_22
  26. a_3_6·b_3_10 + a_2_4·b_1_2·b_3_10 + a_2_4·b_2_5·b_1_22 + a_2_4·b_2_52
       + a_2_4·b_1_2·a_3_6 + a_2_42·b_2_5
  27. b_3_102 + b_2_52·b_1_22 + b_2_53 + a_3_7·b_3_10 + b_2_5·a_1_1·b_3_10
       + b_2_5·a_1_1·b_3_8 + b_2_5·a_1_1·b_1_23 + b_2_52·a_1_1·b_1_2 + a_2_4·b_1_2·b_3_8
       + a_2_4·b_2_5·b_1_22 + c_4_17·a_1_12
  28. b_3_82 + b_2_5·b_1_24 + a_1_1·b_1_22·b_3_8 + c_4_18·a_1_12
  29. a_3_7·b_3_10 + b_2_5·a_1_1·b_3_8 + b_2_5·a_1_1·b_1_23 + a_2_4·b_1_2·b_3_8
       + a_2_4·b_2_5·b_1_22 + b_4_16·a_1_12 + a_2_4·b_1_2·a_3_6 + a_2_4·b_1_2·a_3_7
       + a_2_42·b_2_5
  30. b_3_102 + b_2_52·b_1_22 + b_2_53 + b_2_5·a_1_1·b_3_10 + b_2_52·a_1_1·b_1_2
       + a_1_1·a_5_20 + a_2_42·b_2_5
  31. a_1_0·a_5_20
  32. b_3_102 + b_3_8·b_3_10 + b_2_5·b_1_2·b_3_8 + b_2_53 + a_1_1·b_5_29 + b_2_5·a_1_1·b_3_8
       + b_2_5·a_1_1·b_1_23 + b_2_52·a_1_1·b_1_2 + a_2_4·b_1_2·a_3_7 + c_4_17·a_1_1·b_1_2
  33. a_1_0·b_5_29 + c_4_17·a_1_0·b_1_2
  34. b_1_22·a_5_20 + a_1_1·b_1_23·b_3_8 + b_4_16·a_3_7 + b_2_5·a_1_1·b_1_2·b_3_8
       + a_2_4·b_1_25 + a_2_4·b_2_5·b_1_23 + b_4_16·a_1_12·b_1_2 + a_2_4·b_1_22·a_3_7
       + a_2_42·b_2_5·b_1_2 + c_4_17·a_1_1·b_1_22
  35. b_4_16·a_3_6 + b_2_5·a_5_20 + b_2_5·a_1_1·b_1_2·b_3_10 + b_2_5·a_1_1·b_1_2·b_3_8
       + b_2_5·b_4_16·a_1_1 + b_2_52·a_1_1·b_1_22 + a_2_4·b_2_5·b_1_23
       + a_2_4·b_2_52·b_1_2 + a_2_4·a_5_20 + a_2_42·b_3_10 + a_2_42·b_1_23
       + b_2_5·c_4_17·a_1_1 + c_4_17·a_1_13
  36. b_1_22·b_5_29 + b_4_16·b_3_10 + b_4_16·b_3_8 + b_2_5·b_5_29 + b_2_5·b_4_16·b_1_2
       + b_4_16·a_3_6 + b_2_5·a_5_20 + b_2_5·a_1_1·b_1_24 + b_2_52·a_1_1·b_1_22
       + b_2_53·a_1_1 + a_2_4·b_2_5·b_1_23 + a_2_4·b_2_52·b_1_2 + b_4_16·a_1_12·b_1_2
       + a_2_4·b_1_22·a_3_7 + a_2_42·b_1_23 + c_4_17·b_1_23 + b_2_5·c_4_17·b_1_2
       + b_2_5·c_4_18·a_1_1 + c_4_18·a_1_12·b_1_2 + c_4_17·a_1_12·b_1_2 + c_4_18·a_1_13
  37. b_4_16·b_3_10 + b_2_5·b_5_29 + b_2_5·b_4_16·b_1_2 + a_1_1·b_1_2·b_5_29
       + a_1_1·b_1_23·b_3_8 + b_4_16·a_3_6 + b_4_16·a_1_1·b_1_22 + b_2_5·a_5_20
       + b_2_5·a_1_1·b_1_24 + b_2_5·b_4_16·a_1_1 + b_2_52·a_1_1·b_1_22
       + a_2_4·b_2_5·b_1_23 + a_2_4·b_2_52·b_1_2 + b_4_16·a_1_12·b_1_2 + a_2_42·b_3_8
       + a_2_42·b_1_23 + a_2_42·b_2_5·b_1_2 + b_2_5·c_4_17·b_1_2
  38. b_4_16·a_3_6 + b_2_5·a_5_20 + b_2_5·a_1_1·b_1_2·b_3_10 + b_2_5·a_1_1·b_1_2·b_3_8
       + b_2_5·b_4_16·a_1_1 + b_2_52·a_1_1·b_1_22 + a_2_4·b_2_5·b_1_23
       + a_2_4·b_2_52·b_1_2 + a_1_12·b_5_29 + a_2_42·b_3_10 + a_2_42·b_2_5·b_1_2
       + b_2_5·c_4_17·a_1_1 + c_4_17·a_1_12·b_1_2 + c_4_17·a_1_13
  39. b_2_5·a_5_20 + b_2_5·a_1_1·b_1_2·b_3_10 + b_2_5·a_1_1·b_1_2·b_3_8 + b_2_5·b_4_16·a_1_1
       + b_2_52·a_1_1·b_1_22 + a_2_4·b_5_29 + a_2_4·b_2_5·b_1_23 + a_2_4·b_2_52·b_1_2
       + a_2_42·b_3_10 + a_2_42·b_2_5·b_1_2 + b_2_5·c_4_17·a_1_1 + a_2_4·c_4_17·b_1_2
       + c_4_17·a_1_13
  40. b_1_25·b_3_8 + b_4_16·b_1_24 + b_4_162 + b_2_5·b_1_26 + b_2_5·b_4_16·b_1_22
       + b_2_52·b_1_2·b_3_8 + b_2_52·b_1_24 + b_2_54 + b_4_16·a_1_1·b_1_23
       + b_2_5·b_4_16·a_1_1·b_1_2 + b_2_53·a_1_1·b_1_2 + a_2_4·b_1_23·b_3_8
       + a_2_4·b_4_16·b_1_22 + a_2_4·b_2_5·b_1_24 + a_2_4·b_2_52·b_1_22
       + a_2_4·b_1_23·a_3_7 + a_2_42·b_1_2·b_3_8 + a_2_42·b_2_5·b_1_22 + c_4_17·b_1_24
       + b_2_52·c_4_18 + c_4_18·a_1_12·b_1_22 + c_4_17·a_1_12·b_1_22 + a_2_42·c_4_18
  41. a_3_7·a_5_20 + c_4_17·a_1_12·b_1_22
  42. a_3_6·a_5_20 + a_2_42·b_1_2·b_3_10 + a_2_42·b_1_2·b_3_8 + a_2_42·b_4_16
       + a_2_42·b_2_5·b_1_22
  43. b_1_25·b_3_8 + b_4_16·b_1_24 + b_4_162 + b_2_5·b_1_26 + b_2_5·b_4_16·b_1_22
       + b_2_52·b_1_2·b_3_8 + b_2_52·b_1_24 + b_2_54 + b_3_8·a_5_20 + b_4_16·a_1_1·b_3_8
       + b_4_16·a_1_1·b_1_23 + b_2_5·a_1_1·b_1_25 + b_2_5·b_4_16·a_1_1·b_1_2
       + b_2_52·a_1_1·b_1_23 + b_2_53·a_1_1·b_1_2 + a_2_4·b_2_5·b_1_2·b_3_8
       + a_2_4·b_2_5·b_1_24 + a_2_4·b_2_52·b_1_22 + a_2_4·b_1_2·a_5_20
       + a_2_42·b_1_2·b_3_10 + a_2_42·b_2_5·b_1_22 + c_4_17·b_1_24 + b_2_52·c_4_18
       + c_4_17·a_1_1·b_3_8 + c_4_18·a_1_12·b_1_22 + c_4_17·a_1_12·b_1_22
       + a_2_42·c_4_18 + c_4_18·a_1_13·b_1_2 + c_4_17·a_1_13·b_1_2
  44. b_1_25·b_3_8 + b_4_16·b_1_24 + b_4_162 + b_2_5·b_1_26 + b_2_5·b_4_16·b_1_22
       + b_2_52·b_1_2·b_3_8 + b_2_52·b_1_24 + b_2_54 + a_3_7·b_5_29 + b_4_16·a_1_1·b_3_8
       + b_4_16·a_1_1·b_1_23 + b_2_5·b_4_16·a_1_1·b_1_2 + b_2_53·a_1_1·b_1_2
       + a_2_4·b_1_23·b_3_8 + a_2_4·b_2_5·b_1_24 + a_2_4·b_2_52·b_1_22
       + b_4_16·a_1_12·b_1_22 + a_2_4·b_1_2·a_5_20 + a_2_42·b_1_2·b_3_8 + a_2_42·b_1_24
       + a_2_42·b_4_16 + a_2_42·b_2_52 + c_4_17·b_1_24 + b_2_52·c_4_18
       + c_4_17·b_1_2·a_3_7 + c_4_18·a_1_12·b_1_22 + c_4_17·a_1_13·b_1_2
  45. b_3_10·b_5_29 + b_2_5·b_1_2·b_5_29 + b_2_52·b_4_16 + b_4_16·a_1_1·b_3_8
       + b_2_5·a_1_1·b_5_29 + b_2_5·a_1_1·b_1_22·b_3_8 + b_2_5·a_1_1·b_1_25
       + b_2_5·b_4_16·a_1_1·b_1_2 + b_2_52·a_1_1·b_3_8 + b_2_52·a_1_1·b_1_23
       + b_2_53·a_1_1·b_1_2 + b_4_16·a_1_12·b_1_22 + a_2_42·b_1_2·b_3_10
       + a_2_42·b_1_2·b_3_8 + c_4_17·b_1_2·b_3_10 + b_2_5·c_4_17·b_1_22
       + c_4_17·a_1_1·b_3_10 + c_4_17·a_1_1·b_3_8 + c_4_17·a_1_12·b_1_22
       + c_4_18·a_1_13·b_1_2
  46. a_3_6·b_5_29 + a_2_4·b_2_5·b_4_16 + a_2_42·b_4_16 + c_4_17·b_1_2·a_3_6
  47. b_3_10·b_5_29 + b_2_5·b_1_2·b_5_29 + b_2_52·b_4_16 + b_3_10·a_5_20 + b_4_16·a_1_1·b_3_8
       + b_2_5·a_1_1·b_1_25 + a_2_4·b_1_2·b_5_29 + a_2_4·b_2_5·b_1_2·b_3_10
       + a_2_4·b_2_5·b_1_2·b_3_8 + a_2_4·b_2_5·b_1_24 + a_2_4·b_2_5·b_4_16
       + a_2_4·b_1_23·a_3_7 + a_2_42·b_4_16 + a_2_42·b_2_5·b_1_22 + c_4_17·b_1_2·b_3_10
       + b_2_5·c_4_17·b_1_22 + c_4_17·a_1_1·b_3_8 + b_2_5·c_4_17·a_1_1·b_1_2
       + a_2_4·c_4_17·b_1_22 + a_2_42·c_4_17 + c_4_18·a_1_13·b_1_2
  48. b_3_10·b_5_29 + b_3_8·b_5_29 + b_2_5·b_1_2·b_5_29 + b_2_5·b_4_16·b_1_22
       + b_2_52·b_4_16 + b_4_16·a_1_1·b_3_8 + b_2_5·a_1_1·b_1_22·b_3_8
       + b_2_52·a_1_1·b_3_10 + b_2_52·a_1_1·b_3_8 + b_2_52·a_1_1·b_1_23
       + b_4_16·a_1_12·b_1_22 + a_2_4·b_1_23·a_3_7 + a_2_42·b_1_2·b_3_10
       + a_2_42·b_2_5·b_1_22 + c_4_17·b_1_2·b_3_10 + c_4_17·b_1_2·b_3_8
       + b_2_5·c_4_17·b_1_22 + c_4_18·a_1_1·b_3_10 + c_4_17·a_1_1·b_3_10
       + b_2_5·c_4_18·a_1_1·b_1_2 + b_2_5·c_4_17·a_1_1·b_1_2 + c_4_17·a_1_12·b_1_22
       + a_2_42·c_4_17 + c_4_17·a_1_13·b_1_2
  49. b_4_16·b_5_29 + b_4_16·b_1_22·b_3_8 + b_2_5·b_1_24·b_3_8 + b_2_5·b_1_27
       + b_2_5·b_4_16·b_3_8 + b_2_52·b_1_22·b_3_8 + b_2_53·b_3_10 + b_2_53·b_1_23
       + b_2_54·b_1_2 + b_4_16·a_5_20 + b_4_16·b_1_22·a_3_7 + b_4_162·a_1_1
       + b_2_5·a_1_1·b_1_2·b_5_29 + b_2_52·a_1_1·b_1_2·b_3_10 + b_2_52·a_1_1·b_1_2·b_3_8
       + b_2_52·b_4_16·a_1_1 + b_2_53·a_1_1·b_1_22 + b_2_54·a_1_1 + a_2_4·b_1_24·b_3_8
       + a_2_4·b_1_27 + a_2_4·b_4_16·b_1_23 + a_2_4·b_2_5·b_1_25
       + a_2_4·b_2_5·b_4_16·b_1_2 + a_2_4·b_2_52·b_3_10 + a_2_4·b_2_52·b_3_8
       + a_2_4·b_2_52·b_1_23 + a_2_4·b_2_53·b_1_2 + b_4_16·a_1_12·b_1_23
       + a_2_4·b_1_24·a_3_7 + a_2_42·b_1_25 + a_2_42·b_2_5·b_3_10 + a_2_42·b_2_5·b_3_8
       + c_4_17·b_1_22·b_3_8 + b_4_16·c_4_17·b_1_2 + b_2_5·c_4_18·b_3_10
       + b_2_52·c_4_18·b_1_2 + c_4_18·a_1_1·b_1_2·b_3_10 + c_4_17·b_1_22·a_3_7
       + c_4_17·a_1_1·b_1_2·b_3_8 + b_2_5·c_4_18·a_1_1·b_1_22 + b_2_52·c_4_18·a_1_1
       + a_2_4·c_4_18·b_3_10 + a_2_4·b_2_5·c_4_18·b_1_2 + c_4_18·a_1_12·b_1_23
  50. b_4_16·a_5_20 + b_4_16·b_1_22·a_3_7 + b_4_16·a_1_1·b_1_2·b_3_8
       + b_4_16·a_1_1·b_1_24 + b_4_162·a_1_1 + b_2_5·a_1_1·b_1_2·b_5_29
       + a_2_4·b_1_24·b_3_8 + a_2_4·b_1_27 + a_2_4·b_4_16·b_3_8 + a_2_4·b_4_16·b_1_23
       + a_2_4·b_2_5·b_1_22·b_3_8 + a_2_4·b_2_5·b_4_16·b_1_2 + a_2_4·b_2_52·b_3_10
       + a_2_4·b_2_52·b_1_23 + a_2_4·b_2_53·b_1_2 + b_4_16·a_1_12·b_1_23
       + a_2_4·b_1_24·a_3_7 + a_2_42·b_5_29 + a_2_42·b_2_5·b_1_23 + c_4_17·b_1_22·a_3_7
       + c_4_17·a_1_1·b_1_24 + b_4_16·c_4_17·a_1_1 + b_2_5·c_4_17·a_1_1·b_1_22
       + a_2_4·c_4_18·b_3_10 + a_2_4·b_2_5·c_4_18·b_1_2 + c_4_17·a_1_12·b_1_23
  51. a_5_202 + c_4_172·a_1_12
  52. b_5_292 + b_2_5·b_4_162 + b_4_16·a_1_1·b_1_22·b_3_8 + b_2_5·a_1_1·b_1_24·b_3_8
       + b_2_5·a_1_1·b_1_27 + b_2_5·b_4_16·a_1_1·b_3_8 + b_2_52·a_1_1·b_1_22·b_3_8
       + b_2_53·a_1_1·b_3_10 + b_2_53·a_1_1·b_1_23 + b_2_54·a_1_1·b_1_2
       + b_4_162·a_1_12 + a_2_4·b_1_25·a_3_7 + a_2_4·b_4_16·b_1_2·a_3_7
       + a_2_42·b_1_2·b_5_29 + a_2_42·b_1_23·b_3_8 + a_2_42·b_1_26
       + a_2_42·b_4_16·b_1_22 + a_2_42·b_2_5·b_1_2·b_3_10 + a_2_42·b_2_5·b_1_24
       + a_2_42·b_2_52·b_1_22 + a_2_42·b_2_53 + c_4_17·a_1_1·b_1_22·b_3_8
       + b_2_5·c_4_18·a_1_1·b_3_10 + b_2_52·c_4_18·a_1_1·b_1_2 + b_4_16·c_4_18·a_1_12
       + a_2_4·c_4_18·b_1_2·a_3_6 + a_2_4·c_4_18·b_1_2·a_3_7 + a_2_42·c_4_18·b_1_22
       + a_2_42·b_2_5·c_4_18 + a_2_42·b_2_5·c_4_17 + c_4_172·b_1_22
       + c_4_17·c_4_18·a_1_12 + c_4_172·a_1_12
  53. a_5_20·b_5_29 + b_4_16·a_1_1·b_1_22·b_3_8 + b_2_5·a_1_1·b_1_24·b_3_8
       + b_2_5·a_1_1·b_1_27 + b_2_5·b_4_16·a_1_1·b_3_8 + b_2_5·b_4_16·a_1_1·b_1_23
       + b_2_52·a_1_1·b_1_22·b_3_8 + b_2_52·b_4_16·a_1_1·b_1_2 + b_2_53·a_1_1·b_3_10
       + b_2_53·a_1_1·b_1_23 + b_2_54·a_1_1·b_1_2 + a_2_4·b_4_16·b_1_2·b_3_8
       + a_2_4·b_4_162 + a_2_4·b_2_5·b_1_2·b_5_29 + b_4_162·a_1_12 + a_2_4·b_1_25·a_3_7
       + a_2_42·b_1_23·b_3_8 + a_2_42·b_1_26 + a_2_42·b_4_16·b_1_22
       + a_2_42·b_2_5·b_1_2·b_3_8 + a_2_42·b_2_52·b_1_22 + c_4_17·b_1_2·a_5_20
       + c_4_17·a_1_1·b_5_29 + c_4_17·a_1_1·b_1_22·b_3_8 + b_2_5·c_4_18·a_1_1·b_3_10
       + b_2_52·c_4_18·a_1_1·b_1_2 + a_2_4·b_2_5·c_4_17·b_1_22 + b_4_16·c_4_17·a_1_12
       + a_2_4·c_4_17·b_1_2·a_3_6 + a_2_4·c_4_17·b_1_2·a_3_7 + a_2_42·c_4_17·b_1_22
       + c_4_172·a_1_1·b_1_2

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 10.
  • 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_17, a Duflot regular element of degree 4
    2. c_4_18, a Duflot regular element of degree 4
    3. b_1_24 + b_2_5·b_1_22 + b_2_52, an element of degree 4
    4. b_3_8 + b_2_5·b_1_2, an element of degree 3
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 4, 8, 11].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -4].
  • We found that there exists some filter regular HSOP formed by the first 2 terms of the above HSOP, together with 2 elements of degree 2.

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. b_1_2 → 0, an element of degree 1
  4. a_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. a_3_7 → 0, an element of degree 3
  7. a_3_6 → 0, an element of degree 3
  8. b_3_8 → 0, an element of degree 3
  9. b_3_10 → 0, an element of degree 3
  10. b_4_16 → 0, an element of degree 4
  11. c_4_17 → c_1_04, an element of degree 4
  12. c_4_18 → c_1_14, an element of degree 4
  13. a_5_20 → 0, an element of degree 5
  14. b_5_29 → 0, an element of degree 5

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. b_1_2 → c_1_2, an element of degree 1
  4. a_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_32, an element of degree 2
  6. a_3_7 → 0, an element of degree 3
  7. a_3_6 → 0, an element of degree 3
  8. b_3_8 → c_1_22·c_1_3, an element of degree 3
  9. b_3_10 → c_1_33 + c_1_2·c_1_32, an element of degree 3
  10. b_4_16 → c_1_34 + c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_23·c_1_3 + c_1_12·c_1_32
       + c_1_02·c_1_22, an element of degree 4
  11. c_4_17 → c_1_22·c_1_32 + c_1_12·c_1_32 + c_1_02·c_1_32 + c_1_02·c_1_22 + c_1_04, an element of degree 4
  12. c_4_18 → c_1_12·c_1_22 + c_1_14, an element of degree 4
  13. a_5_20 → 0, an element of degree 5
  14. b_5_29 → c_1_35 + c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_12·c_1_33 + c_1_12·c_1_2·c_1_32
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3 + c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5

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