Cohomology of group number 328 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 2 conjugacy classes of maximal elementary abelian subgroups, which are all 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  +  2·t4  +  t2  +  t  +  1
    (t  +  1)2 · (t  −  1)4 · (t2  +  1)2
  • The a-invariants are -∞,-∞,-5,-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 15 minimal generators of maximal degree 6:

  1. a_1_1, a nilpotent element of degree 1
  2. b_1_0, an element of degree 1
  3. b_1_2, an element of degree 1
  4. b_2_4, an element of degree 2
  5. b_2_5, an element of degree 2
  6. b_3_7, an element of degree 3
  7. b_3_8, an element of degree 3
  8. b_4_9, an element of degree 4
  9. b_4_11, an element of degree 4
  10. b_4_12, an element of degree 4
  11. b_4_13, an element of degree 4
  12. c_4_14, a Duflot regular element of degree 4
  13. c_4_15, a Duflot regular element of degree 4
  14. b_5_25, an element of degree 5
  15. b_6_37, an 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 65 minimal relations of maximal degree 12:

  1. a_1_1·b_1_0
  2. b_1_0·b_1_2
  3. a_1_13
  4. b_2_4·b_1_2 + a_1_12·b_1_2
  5. b_2_4·a_1_1 + a_1_12·b_1_2
  6. b_2_5·a_1_1 + a_1_12·b_1_2
  7. b_1_2·b_3_7
  8. a_1_1·b_3_7
  9. b_1_2·b_3_8
  10. a_1_1·b_3_8
  11. b_1_0·b_3_8 + b_2_42
  12. b_4_9·b_1_0 + b_2_4·b_2_5·b_1_0
  13. b_4_11·b_1_2 + b_4_9·a_1_1
  14. b_4_11·a_1_1
  15. b_4_11·b_1_0 + b_2_4·b_3_7
  16. b_4_12·a_1_1
  17. b_4_12·b_1_0 + b_2_5·b_3_7
  18. b_4_13·a_1_1
  19. b_4_13·b_1_0 + b_2_4·b_3_8 + b_2_4·b_3_7
  20. b_3_82 + b_2_42·b_2_5 + b_2_43 + c_4_14·b_1_02
  21. b_3_72 + c_4_15·b_1_02
  22. b_2_4·b_4_9 + b_2_42·b_2_5
  23. b_3_7·b_3_8 + b_2_4·b_4_11
  24. b_4_12·b_1_22 + b_2_5·b_4_9 + b_2_4·b_2_52 + b_4_9·a_1_1·b_1_2
  25. b_2_5·b_4_11 + b_2_4·b_4_12
  26. b_3_82 + b_3_7·b_3_8 + b_2_4·b_4_13
  27. b_1_2·b_5_25 + b_4_13·b_1_22 + b_4_9·b_1_22 + b_2_5·b_4_9 + b_2_4·b_2_52
       + c_4_14·b_1_22 + c_4_14·a_1_1·b_1_2
  28. a_1_1·b_5_25 + b_4_9·a_1_1·b_1_2 + c_4_14·a_1_1·b_1_2 + c_4_14·a_1_12
  29. b_3_7·b_3_8 + b_1_0·b_5_25 + b_2_4·b_1_0·b_3_7 + b_2_4·b_2_5·b_1_02 + b_2_42·b_2_5
       + b_2_43
  30. b_4_9·b_3_7 + b_2_4·b_2_5·b_3_7
  31. b_4_9·b_3_8 + b_2_4·b_2_5·b_3_8
  32. b_4_11·b_3_7 + b_2_4·c_4_15·b_1_0
  33. b_4_12·b_3_7 + b_2_5·c_4_15·b_1_0
  34. b_4_13·b_3_7 + b_4_11·b_3_8 + b_2_4·c_4_15·b_1_0
  35. b_4_13·b_3_8 + b_4_11·b_3_8 + b_2_4·b_2_5·b_3_8 + b_2_42·b_2_5·b_1_0 + b_2_43·b_1_0
       + c_4_14·b_1_03 + b_2_4·c_4_14·b_1_0
  36. b_4_12·b_3_8 + b_2_5·b_5_25 + b_2_5·b_4_13·b_1_2 + b_2_5·b_4_12·b_1_2
       + b_2_5·b_4_9·b_1_2 + b_2_52·b_3_8 + b_2_4·b_2_5·b_3_8 + b_2_4·b_2_5·b_3_7
       + b_2_4·b_2_52·b_1_0 + b_2_5·c_4_14·b_1_2 + c_4_14·a_1_12·b_1_2
  37. b_4_11·b_3_8 + b_2_4·b_5_25 + b_2_4·b_2_5·b_3_8 + b_2_42·b_3_7 + b_2_43·b_1_0
       + c_4_14·b_1_03
  38. b_6_37·a_1_1
  39. b_6_37·b_1_0 + b_4_11·b_3_8 + b_2_5·b_1_02·b_3_7 + b_2_52·b_3_7 + b_2_4·b_2_5·b_3_7
       + b_2_4·b_2_52·b_1_0 + b_2_42·b_1_03 + b_2_42·b_2_5·b_1_0 + b_2_43·b_1_0
       + c_4_14·b_1_03 + b_2_5·c_4_15·b_1_0 + b_2_5·c_4_14·b_1_0 + b_2_4·c_4_14·b_1_0
  40. b_4_92 + b_2_42·b_2_52 + c_4_15·b_1_24
  41. b_4_112 + b_2_42·c_4_15
  42. b_4_9·b_4_11 + b_2_42·b_4_12 + c_4_15·a_1_1·b_1_23
  43. b_4_122 + b_2_52·c_4_15
  44. b_4_11·b_4_12 + b_2_4·b_2_5·c_4_15
  45. b_4_9·b_4_12 + b_2_4·b_2_5·b_4_12 + b_2_5·c_4_15·b_1_22 + c_4_15·a_1_1·b_1_23
  46. b_4_132 + b_2_52·b_4_9 + b_2_4·b_2_53 + b_2_42·b_2_52 + b_2_44
       + b_2_5·c_4_14·b_1_02 + b_2_4·c_4_14·b_1_02 + b_2_42·c_4_15 + b_2_42·c_4_14
  47. b_4_11·b_4_13 + b_4_9·b_4_11 + b_2_42·b_4_11 + c_4_14·b_1_0·b_3_7 + b_2_42·c_4_15
       + c_4_15·a_1_1·b_1_23
  48. b_3_7·b_5_25 + b_4_9·b_4_11 + b_2_4·b_2_5·b_1_0·b_3_7 + b_2_42·b_4_11
       + b_2_4·c_4_15·b_1_02 + b_2_42·c_4_15 + c_4_15·a_1_1·b_1_23
  49. b_3_8·b_5_25 + b_4_9·b_4_11 + b_2_42·b_2_52 + b_2_43·b_2_5 + b_2_44
       + c_4_14·b_1_0·b_3_7 + b_2_5·c_4_14·b_1_02 + b_2_4·c_4_14·b_1_02
       + c_4_15·a_1_1·b_1_23
  50. b_4_12·b_4_13 + b_2_5·b_6_37 + b_2_52·b_1_0·b_3_7 + b_2_52·b_4_12 + b_2_4·b_2_5·b_4_12
       + b_2_4·b_2_53 + b_2_42·b_2_52 + b_2_43·b_1_02 + b_2_43·b_2_5 + b_2_44
       + c_4_14·b_1_04 + b_2_5·c_4_14·b_1_02 + b_2_52·c_4_15 + b_2_52·c_4_14
       + b_2_4·b_2_5·c_4_15 + b_2_4·b_2_5·c_4_14
  51. b_6_37·b_1_22 + b_4_9·b_4_13 + b_4_9·b_4_11 + b_2_52·b_4_9 + b_2_4·b_2_53
       + b_2_42·b_2_52 + b_2_43·b_2_5 + b_2_5·c_4_15·b_1_22 + b_2_5·c_4_14·b_1_22
       + b_2_5·c_4_14·b_1_02 + c_4_15·a_1_1·b_1_23
  52. b_2_4·b_6_37 + b_2_4·b_2_5·b_1_0·b_3_7 + b_2_4·b_2_5·b_4_12 + b_2_42·b_4_11
       + b_2_42·b_2_52 + b_2_43·b_1_02 + b_2_43·b_2_5 + b_2_44 + c_4_14·b_1_0·b_3_7
       + b_2_4·c_4_14·b_1_02 + b_2_4·b_2_5·c_4_15 + b_2_4·b_2_5·c_4_14 + b_2_42·c_4_14
  53. b_4_13·b_5_25 + b_4_12·b_5_25 + b_4_9·b_4_13·b_1_2 + b_2_52·b_5_25
       + b_2_52·b_4_13·b_1_2 + b_2_52·b_4_12·b_1_2 + b_2_53·b_3_8 + b_2_4·b_2_5·b_5_25
       + b_2_4·b_2_52·b_3_8 + b_2_4·b_2_53·b_1_0 + b_2_42·b_2_5·b_3_7
       + b_2_42·b_2_52·b_1_0 + b_2_43·b_3_7 + b_2_43·b_2_5·b_1_0 + b_2_44·b_1_0
       + c_4_14·b_1_02·b_3_7 + b_4_13·c_4_14·b_1_2 + b_4_12·c_4_14·b_1_2 + b_2_5·c_4_15·b_3_8
       + b_2_5·c_4_15·b_1_23 + b_2_52·c_4_15·b_1_2 + b_2_52·c_4_14·b_1_2
       + b_2_4·c_4_15·b_3_8 + b_2_4·c_4_14·b_3_7 + b_2_4·c_4_14·b_1_03
       + b_2_4·b_2_5·c_4_15·b_1_0 + b_2_4·b_2_5·c_4_14·b_1_0 + b_2_42·c_4_15·b_1_0
       + b_2_42·c_4_14·b_1_0 + c_4_15·a_1_1·b_1_24
  54. b_4_11·b_5_25 + b_2_4·b_2_5·b_5_25 + b_2_4·b_2_52·b_3_8 + b_2_42·b_2_5·b_3_7
       + b_2_43·b_3_7 + b_2_43·b_2_5·b_1_0 + c_4_14·b_1_02·b_3_7 + b_2_5·c_4_14·b_1_03
       + b_2_4·c_4_15·b_3_8 + b_2_42·c_4_15·b_1_0 + c_4_15·a_1_1·b_1_24
       + b_4_9·c_4_14·a_1_1
  55. b_4_9·b_5_25 + b_4_9·b_4_13·b_1_2 + b_2_4·b_2_5·b_5_25 + c_4_15·b_1_25
       + b_4_9·c_4_14·b_1_2 + b_2_5·c_4_15·b_1_23 + b_4_9·c_4_14·a_1_1
  56. b_4_13·b_5_25 + b_4_9·b_4_13·b_1_2 + b_2_5·b_6_37·b_1_2 + b_2_52·b_4_12·b_1_2
       + b_2_52·b_4_9·b_1_2 + b_2_4·b_2_52·b_3_8 + b_2_42·b_2_52·b_1_0 + b_2_43·b_3_7
       + b_2_44·b_1_0 + c_4_14·b_1_02·b_3_7 + b_4_13·c_4_14·b_1_2 + b_2_5·c_4_14·b_1_03
       + b_2_52·c_4_15·b_1_2 + b_2_52·c_4_14·b_1_2 + b_2_4·c_4_15·b_3_8 + b_2_4·c_4_14·b_3_7
       + b_2_4·c_4_14·b_1_03 + b_2_4·b_2_5·c_4_14·b_1_0 + b_2_42·c_4_15·b_1_0
       + b_2_42·c_4_14·b_1_0
  57. b_6_37·b_3_7 + b_2_4·b_2_52·b_3_7 + b_2_42·b_1_02·b_3_7 + b_2_42·b_2_5·b_3_7
       + b_2_43·b_3_7 + c_4_14·b_1_02·b_3_7 + b_2_5·c_4_15·b_3_7 + b_2_5·c_4_15·b_1_03
       + b_2_5·c_4_14·b_3_7 + b_2_52·c_4_15·b_1_0 + b_2_4·c_4_15·b_3_8 + b_2_4·c_4_14·b_3_7
       + b_2_4·b_2_5·c_4_15·b_1_0
  58. b_6_37·b_3_8 + b_2_52·b_5_25 + b_2_52·b_4_13·b_1_2 + b_2_52·b_4_12·b_1_2
       + b_2_52·b_4_9·b_1_2 + b_2_53·b_3_8 + b_2_4·b_2_52·b_3_7 + b_2_4·b_2_53·b_1_0
       + b_2_42·b_2_52·b_1_0 + b_2_43·b_3_7 + c_4_14·b_1_02·b_3_7 + b_2_5·c_4_15·b_3_8
       + b_2_5·c_4_14·b_3_8 + b_2_5·c_4_14·b_1_03 + b_2_52·c_4_14·b_1_2
       + b_2_4·c_4_14·b_3_8 + b_2_4·c_4_14·b_3_7 + b_2_4·c_4_14·b_1_03
       + b_2_42·c_4_14·b_1_0
  59. b_5_252 + b_2_52·b_4_9·b_1_22 + b_2_42·b_2_53 + b_2_43·b_2_52
       + b_2_44·b_1_02 + c_4_15·b_1_26 + b_2_5·c_4_14·b_1_04 + b_2_52·c_4_15·b_1_22
       + b_2_52·c_4_14·b_1_02 + b_2_4·c_4_14·b_1_04 + b_2_42·c_4_15·b_1_02
       + b_2_42·c_4_14·b_1_02 + b_2_42·b_2_5·c_4_15 + b_2_43·c_4_15
       + c_4_14·c_4_15·b_1_02 + c_4_142·b_1_22 + c_4_142·a_1_12
  60. b_4_13·b_6_37 + b_2_52·b_6_37 + b_2_53·b_1_0·b_3_7 + b_2_53·b_4_12
       + b_2_4·b_2_52·b_4_12 + b_2_4·b_2_54 + b_2_42·b_2_5·b_4_12 + b_2_43·b_1_0·b_3_7
       + b_2_43·b_4_12 + b_2_43·b_2_52 + b_2_44·b_1_02 + b_2_44·b_2_5 + b_2_45
       + b_2_5·c_4_14·b_1_04 + b_2_5·b_4_13·c_4_15 + b_2_5·b_4_13·c_4_14
       + b_2_52·c_4_15·b_1_22 + b_2_53·c_4_15 + b_2_53·c_4_14 + b_2_4·c_4_14·b_1_04
       + b_2_4·b_2_5·c_4_15·b_1_02 + b_2_4·b_2_5·c_4_14·b_1_02 + b_2_4·b_2_52·c_4_15
       + b_2_4·b_2_52·c_4_14 + b_2_42·c_4_14·b_1_02 + b_2_42·b_2_5·c_4_14
       + b_2_43·c_4_15 + c_4_14·c_4_15·b_1_02 + c_4_142·b_1_02
  61. b_4_12·b_6_37 + b_2_4·b_2_52·b_4_12 + b_2_42·b_2_5·b_4_12 + b_2_43·b_1_0·b_3_7
       + b_2_43·b_4_12 + b_2_43·b_4_11 + c_4_14·b_1_03·b_3_7 + b_2_5·c_4_14·b_1_0·b_3_7
       + b_2_5·b_4_13·c_4_15 + b_2_5·b_4_12·c_4_15 + b_2_5·b_4_12·c_4_14
       + b_2_52·c_4_15·b_1_02 + b_2_53·c_4_15 + b_2_4·b_4_12·c_4_15 + b_2_4·b_4_12·c_4_14
       + b_2_4·b_2_52·c_4_15
  62. b_4_11·b_6_37 + b_2_42·b_2_5·b_4_12 + b_2_43·b_1_0·b_3_7 + b_2_43·b_4_12
       + b_2_43·b_4_11 + b_2_4·c_4_14·b_1_0·b_3_7 + b_2_4·b_4_12·c_4_15 + b_2_4·b_4_12·c_4_14
       + b_2_4·b_4_11·c_4_14 + b_2_4·b_2_5·c_4_15·b_1_02 + b_2_4·b_2_52·c_4_15
       + b_2_43·c_4_15 + c_4_14·c_4_15·b_1_02
  63. b_4_9·b_6_37 + b_2_4·b_2_52·b_1_0·b_3_7 + b_2_4·b_2_52·b_4_12 + b_2_42·b_2_53
       + b_2_43·b_4_12 + b_2_43·b_2_52 + b_2_44·b_1_02 + b_2_44·b_2_5 + b_2_45
       + b_4_13·c_4_15·b_1_22 + b_2_5·c_4_14·b_1_0·b_3_7 + b_2_5·b_4_9·c_4_15
       + b_2_5·b_4_9·c_4_14 + b_2_52·c_4_15·b_1_22 + b_2_4·c_4_14·b_1_04
       + b_2_4·b_2_5·c_4_14·b_1_02 + b_2_42·b_2_5·c_4_14
  64. b_6_37·b_5_25 + b_2_52·b_6_37·b_1_2 + b_2_53·b_5_25 + b_2_53·b_4_13·b_1_2
       + b_2_53·b_4_9·b_1_2 + b_2_54·b_3_8 + b_2_4·b_2_52·b_1_02·b_3_7
       + b_2_4·b_2_54·b_1_0 + b_2_42·b_2_53·b_1_0 + b_2_43·b_1_02·b_3_7
       + b_2_43·b_2_5·b_3_7 + b_2_43·b_2_52·b_1_0 + b_2_44·b_1_03 + b_2_44·b_2_5·b_1_0
       + b_2_45·b_1_0 + c_4_14·b_6_37·b_1_2 + b_4_13·c_4_15·b_1_23 + b_2_5·c_4_15·b_5_25
       + b_2_5·c_4_14·b_5_25 + b_2_5·c_4_14·b_1_02·b_3_7 + b_2_5·b_4_13·c_4_15·b_1_2
       + b_2_52·c_4_15·b_3_8 + b_2_4·c_4_14·b_5_25 + b_2_4·c_4_14·b_1_02·b_3_7
       + b_2_4·c_4_14·b_1_05 + b_2_4·b_2_5·c_4_15·b_1_03 + b_2_4·b_2_5·c_4_14·b_3_7
       + b_2_4·b_2_5·c_4_14·b_1_03 + b_2_4·b_2_52·c_4_15·b_1_0 + b_2_42·c_4_14·b_1_03
       + b_2_42·b_2_5·c_4_14·b_1_0 + b_2_43·c_4_14·b_1_0 + b_2_5·c_4_14·c_4_15·b_1_2
       + b_2_5·c_4_142·b_1_2 + b_2_4·c_4_14·c_4_15·b_1_0 + c_4_14·c_4_15·a_1_12·b_1_2
       + c_4_142·a_1_12·b_1_2
  65. b_6_372 + b_2_42·b_2_54 + b_2_44·b_1_04 + b_2_44·b_2_52 + b_2_46
       + b_2_52·c_4_15·b_1_04 + b_2_52·b_4_9·c_4_15 + b_2_54·c_4_15
       + b_2_4·b_2_53·c_4_15 + b_2_44·c_4_15 + c_4_142·b_1_04
       + b_2_5·c_4_14·c_4_15·b_1_02 + b_2_52·c_4_152 + b_2_52·c_4_142
       + b_2_4·c_4_14·c_4_15·b_1_02 + b_2_42·c_4_14·c_4_15 + b_2_42·c_4_142

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_14, a Duflot regular element of degree 4
    2. c_4_15, a Duflot regular element of degree 4
    3. b_1_22 + b_1_02 + b_2_5, an element of degree 2
    4. b_1_22 + b_1_02, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 3, 6, 8].
  • 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_1 → 0, an element of degree 1
  2. b_1_0 → 0, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_7 → 0, an element of degree 3
  7. b_3_8 → 0, an element of degree 3
  8. b_4_9 → 0, an element of degree 4
  9. b_4_11 → 0, an element of degree 4
  10. b_4_12 → 0, an element of degree 4
  11. b_4_13 → 0, an element of degree 4
  12. c_4_14 → c_1_14, an element of degree 4
  13. c_4_15 → c_1_04, an element of degree 4
  14. b_5_25 → 0, an element of degree 5
  15. b_6_37 → 0, an element of degree 6

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

  1. a_1_1 → 0, an element of degree 1
  2. b_1_0 → c_1_2, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_2_4 → c_1_1·c_1_2, an element of degree 2
  5. b_2_5 → c_1_32 + c_1_2·c_1_3, an element of degree 2
  6. b_3_7 → c_1_0·c_1_22 + c_1_02·c_1_2, an element of degree 3
  7. b_3_8 → c_1_12·c_1_2, an element of degree 3
  8. b_4_9 → c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3, an element of degree 4
  9. b_4_11 → c_1_0·c_1_1·c_1_22 + c_1_02·c_1_1·c_1_2, an element of degree 4
  10. b_4_12 → c_1_0·c_1_2·c_1_32 + c_1_0·c_1_22·c_1_3 + c_1_02·c_1_32 + c_1_02·c_1_2·c_1_3, an element of degree 4
  11. b_4_13 → c_1_13·c_1_2 + c_1_0·c_1_1·c_1_22 + c_1_02·c_1_1·c_1_2, an element of degree 4
  12. c_4_14 → c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3 + c_1_13·c_1_2 + c_1_14, an element of degree 4
  13. c_4_15 → c_1_02·c_1_22 + c_1_04, an element of degree 4
  14. b_5_25 → c_1_1·c_1_22·c_1_32 + c_1_1·c_1_23·c_1_3 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_22 + c_1_0·c_1_1·c_1_23
       + c_1_0·c_1_12·c_1_22 + c_1_02·c_1_1·c_1_22 + c_1_02·c_1_12·c_1_2, an element of degree 5
  15. b_6_37 → c_1_1·c_1_2·c_1_34 + c_1_1·c_1_23·c_1_32 + c_1_12·c_1_34
       + c_1_12·c_1_22·c_1_32 + c_1_12·c_1_24 + c_1_14·c_1_32 + c_1_14·c_1_2·c_1_3
       + c_1_15·c_1_2 + c_1_0·c_1_2·c_1_34 + c_1_0·c_1_24·c_1_3
       + c_1_0·c_1_1·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_23·c_1_3 + c_1_0·c_1_13·c_1_22
       + c_1_02·c_1_34 + c_1_02·c_1_22·c_1_32 + c_1_02·c_1_1·c_1_2·c_1_32
       + c_1_02·c_1_1·c_1_22·c_1_3 + c_1_02·c_1_13·c_1_2 + c_1_04·c_1_32
       + c_1_04·c_1_2·c_1_3, an element of degree 6

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

  1. a_1_1 → 0, an element of degree 1
  2. b_1_0 → 0, an element of degree 1
  3. b_1_2 → c_1_2, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_32 + c_1_2·c_1_3, an element of degree 2
  6. b_3_7 → 0, an element of degree 3
  7. b_3_8 → 0, an element of degree 3
  8. b_4_9 → c_1_02·c_1_22, an element of degree 4
  9. b_4_11 → 0, an element of degree 4
  10. b_4_12 → c_1_02·c_1_32 + c_1_02·c_1_2·c_1_3, an element of degree 4
  11. b_4_13 → c_1_0·c_1_2·c_1_32 + c_1_0·c_1_22·c_1_3, an element of degree 4
  12. c_4_14 → 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 + c_1_02·c_1_22, an element of degree 4
  13. c_4_15 → c_1_04, an element of degree 4
  14. b_5_25 → c_1_1·c_1_22·c_1_32 + c_1_1·c_1_23·c_1_3 + c_1_12·c_1_2·c_1_32
       + c_1_12·c_1_22·c_1_3 + c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_0·c_1_22·c_1_32
       + c_1_0·c_1_23·c_1_3 + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3, an element of degree 5
  15. b_6_37 → c_1_1·c_1_2·c_1_34 + c_1_1·c_1_23·c_1_32 + c_1_12·c_1_34
       + c_1_12·c_1_23·c_1_3 + c_1_14·c_1_32 + c_1_14·c_1_2·c_1_3 + c_1_02·c_1_34
       + c_1_02·c_1_23·c_1_3 + c_1_03·c_1_2·c_1_32 + c_1_03·c_1_22·c_1_3
       + c_1_04·c_1_32 + c_1_04·c_1_2·c_1_3, 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