Cohomology of group number 203 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 3 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 3.
  • The depth exceeds the Duflot bound, which is 2.
  • The Poincaré series is
    t4  +  t3  +  t2  +  1
    (t  +  1) · (t  −  1)4 · (t2  +  1)2
  • The a-invariants are -∞,-∞,-∞,-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 5:

  1. a_1_0, a nilpotent element of degree 1
  2. b_1_1, 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. a_3_4, a nilpotent element of degree 3
  7. b_3_8, an element of degree 3
  8. b_3_9, an element of degree 3
  9. b_3_10, an element of degree 3
  10. b_4_16, an element of degree 4
  11. b_4_17, an element of degree 4
  12. c_4_18, a Duflot regular element of degree 4
  13. c_4_19, a Duflot regular element of degree 4
  14. b_5_30, an element of degree 5
  15. b_5_31, 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 65 minimal relations of maximal degree 10:

  1. a_1_02
  2. a_1_0·b_1_1
  3. b_1_1·b_1_22 + b_1_12·b_1_2
  4. b_2_4·a_1_0
  5. b_2_4·b_1_1
  6. b_2_5·a_1_0
  7. b_2_5·b_1_22 + b_2_5·b_1_1·b_1_2 + b_2_42
  8. a_1_0·a_3_4
  9. b_1_1·a_3_4
  10. a_1_0·b_3_8
  11. a_1_0·b_3_9
  12. b_1_1·b_3_9
  13. a_1_0·b_3_10
  14. b_1_22·b_3_8 + b_1_1·b_1_2·b_3_8 + b_2_42·b_1_2 + b_2_4·a_3_4
  15. b_2_4·b_3_8 + b_2_4·b_2_5·b_1_2 + b_2_5·a_3_4
  16. b_2_4·b_3_9 + b_2_4·b_2_5·b_1_2 + b_2_5·a_3_4
  17. b_1_22·b_3_10 + b_1_22·b_3_9 + b_1_1·b_1_2·b_3_10 + b_2_4·b_2_5·b_1_2 + b_2_5·a_3_4
  18. b_2_5·b_3_9 + b_2_4·b_3_10 + b_2_4·b_2_5·b_1_2 + b_2_5·a_3_4
  19. b_1_22·b_3_9 + b_2_42·b_1_2 + b_4_16·a_1_0 + b_2_4·a_3_4
  20. b_4_16·b_1_1 + b_2_5·b_1_12·b_1_2
  21. b_1_22·b_3_9 + b_2_42·b_1_2 + b_4_17·a_1_0 + b_2_4·a_3_4
  22. b_4_17·b_1_1 + b_2_5·b_3_9 + b_2_5·b_3_8 + b_2_5·b_1_12·b_1_2
  23. a_3_42
  24. a_3_4·b_3_8 + b_2_5·b_1_2·a_3_4
  25. a_3_4·b_3_9 + b_2_5·b_1_2·a_3_4
  26. b_3_8·b_3_9 + b_2_42·b_2_5
  27. b_3_92 + b_2_42·b_2_5
  28. b_2_4·b_1_2·b_3_10 + b_2_42·b_2_5 + b_2_43 + a_3_4·b_3_10
  29. b_3_9·b_3_10 + b_2_4·b_2_52 + b_2_42·b_2_5
  30. b_3_102 + b_3_82 + b_2_5·b_1_1·b_3_10 + b_2_5·b_1_13·b_1_2 + b_2_53
       + c_4_18·b_1_12
  31. b_3_82 + b_2_42·b_2_5 + c_4_19·b_1_12
  32. b_4_17·b_1_22 + b_4_16·b_1_22 + b_2_5·b_1_2·b_3_8 + b_2_4·b_1_2·b_3_10
       + b_2_4·b_4_16 + b_2_43 + b_2_5·b_1_2·a_3_4
  33. b_2_5·b_4_16 + b_2_52·b_1_1·b_1_2 + b_2_4·b_4_17 + b_2_4·b_4_16
  34. a_1_0·b_5_30 + c_4_18·a_1_0·b_1_2
  35. b_1_1·b_5_30 + c_4_18·b_1_1·b_1_2
  36. a_1_0·b_5_31 + c_4_18·a_1_0·b_1_2
  37. b_3_102 + b_3_8·b_3_10 + b_1_1·b_5_31 + b_2_5·b_1_1·b_3_10 + b_2_53 + b_2_4·b_2_52
       + c_4_18·b_1_1·b_1_2
  38. b_4_16·b_3_9 + b_4_16·b_3_8 + b_2_5·b_1_1·b_1_2·b_3_8 + c_4_19·a_1_0·b_1_22
       + c_4_18·a_1_0·b_1_22
  39. b_4_16·b_3_8 + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_4·b_4_17·b_1_2 + b_2_4·b_4_16·b_1_2
       + b_4_17·a_3_4 + b_4_16·a_3_4
  40. b_4_17·b_3_8 + b_4_16·b_3_10 + b_2_5·b_1_1·b_1_2·b_3_10 + b_2_5·b_1_1·b_1_2·b_3_8
       + b_2_5·c_4_19·b_1_1 + c_4_19·a_1_0·b_1_22 + c_4_18·a_1_0·b_1_22
  41. b_4_17·b_3_9 + b_4_16·b_3_10 + b_2_5·b_1_1·b_1_2·b_3_10
  42. b_4_16·b_3_10 + b_4_16·b_3_8 + b_2_5·b_5_30 + b_2_5·b_1_1·b_1_2·b_3_10
       + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_42·b_3_10 + b_2_42·b_2_5·b_1_2 + b_2_4·b_2_5·a_3_4
       + b_2_5·c_4_18·b_1_2 + c_4_19·a_1_0·b_1_22 + c_4_18·a_1_0·b_1_22
  43. b_1_22·b_5_30 + b_2_4·b_4_16·b_1_2 + b_2_43·b_1_2 + b_4_16·a_3_4 + b_2_42·a_3_4
       + c_4_18·b_1_23 + c_4_19·a_1_0·b_1_22 + c_4_18·a_1_0·b_1_22
  44. b_4_16·b_3_8 + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_4·b_5_30 + b_2_42·b_2_5·b_1_2
       + b_2_4·b_2_5·a_3_4 + b_2_4·c_4_18·b_1_2
  45. b_4_17·b_3_10 + b_4_16·b_3_8 + b_2_5·b_5_31 + b_2_5·b_1_1·b_1_2·b_3_10
       + b_2_5·b_1_1·b_1_2·b_3_8 + b_2_52·b_1_12·b_1_2 + b_2_5·c_4_19·b_1_1
       + b_2_5·c_4_18·b_1_2 + b_2_5·c_4_18·b_1_1 + c_4_19·a_1_0·b_1_22
       + c_4_18·a_1_0·b_1_22
  46. b_1_22·b_5_31 + b_1_1·b_1_2·b_5_31 + b_4_16·b_3_8 + b_2_5·b_1_1·b_1_2·b_3_8
       + c_4_18·b_1_23 + c_4_18·b_1_12·b_1_2
  47. b_4_16·b_3_10 + b_4_16·b_3_8 + b_2_5·b_1_1·b_1_2·b_3_10 + b_2_5·b_1_1·b_1_2·b_3_8
       + b_2_4·b_5_31 + b_2_4·c_4_18·b_1_2 + c_4_19·a_1_0·b_1_22 + c_4_18·a_1_0·b_1_22
  48. b_4_162 + b_2_52·b_1_13·b_1_2 + b_2_4·b_1_26 + b_2_42·b_4_16 + c_4_19·b_1_24
       + c_4_19·b_1_13·b_1_2 + c_4_18·b_1_24 + c_4_18·b_1_13·b_1_2 + b_2_42·c_4_19
  49. b_4_172 + b_2_52·b_1_13·b_1_2 + b_2_4·b_1_26 + b_2_4·b_2_5·b_4_17 + b_2_42·b_4_17
       + b_2_43·b_1_22 + c_4_19·b_1_24 + c_4_19·b_1_13·b_1_2 + c_4_18·b_1_24
       + c_4_18·b_1_13·b_1_2 + b_2_52·c_4_19 + b_2_42·c_4_18
  50. b_4_16·b_4_17 + b_2_52·b_1_2·b_3_8 + b_2_52·b_1_13·b_1_2 + b_2_4·b_1_26
       + b_2_42·b_1_24 + b_2_42·b_4_17 + b_2_42·b_2_52 + b_2_5·a_3_4·b_3_10
       + b_2_4·a_3_4·b_3_10 + b_2_4·b_2_5·b_1_2·a_3_4 + c_4_19·b_1_24 + c_4_19·b_1_13·b_1_2
       + c_4_18·b_1_24 + c_4_18·b_1_13·b_1_2 + b_2_4·c_4_19·b_1_22
       + b_2_4·c_4_18·b_1_22 + b_2_4·b_2_5·c_4_19 + b_2_42·c_4_19
  51. b_3_10·b_5_30 + b_2_4·b_2_5·b_4_17 + b_2_42·b_2_52 + b_2_43·b_2_5
       + c_4_18·b_1_2·b_3_10
  52. a_3_4·b_5_30 + b_4_17·b_1_2·a_3_4 + b_4_16·b_1_2·a_3_4 + b_2_4·b_2_5·b_1_2·a_3_4
       + c_4_18·b_1_2·a_3_4
  53. b_3_8·b_5_30 + b_2_42·b_4_17 + b_2_42·b_4_16 + b_2_43·b_2_5 + c_4_18·b_1_2·b_3_8
  54. b_3_9·b_5_30 + b_2_42·b_4_17 + b_2_42·b_4_16 + b_2_43·b_2_5 + c_4_18·b_1_2·b_3_9
  55. b_3_10·b_5_31 + b_2_5·b_1_1·b_5_31 + b_2_5·b_1_12·b_1_2·b_3_10
       + b_2_5·b_1_12·b_1_2·b_3_8 + b_2_52·b_1_13·b_1_2 + b_2_52·b_4_17
       + b_2_53·b_1_1·b_1_2 + c_4_19·b_1_1·b_3_10 + c_4_19·b_1_1·b_3_8 + c_4_18·b_1_2·b_3_10
       + c_4_18·b_1_1·b_3_10 + c_4_18·b_1_1·b_3_8 + b_2_5·c_4_19·b_1_12
       + b_2_5·c_4_18·b_1_1·b_1_2 + b_2_5·c_4_18·b_1_12
  56. b_2_4·b_1_2·b_5_31 + b_2_42·b_4_17 + b_2_42·b_4_16 + a_3_4·b_5_31
       + b_2_4·c_4_18·b_1_22 + c_4_18·b_1_2·a_3_4
  57. b_3_8·b_5_31 + b_2_5·b_1_12·b_1_2·b_3_8 + b_2_4·b_2_5·b_4_17 + b_2_42·b_4_17
       + b_2_42·b_4_16 + c_4_19·b_1_1·b_3_10 + c_4_19·b_1_1·b_3_8 + c_4_18·b_1_2·b_3_8
       + c_4_18·b_1_1·b_3_8
  58. b_3_9·b_5_31 + b_2_4·b_2_5·b_4_17 + b_2_42·b_4_17 + b_2_42·b_4_16 + c_4_18·b_1_2·b_3_9
  59. b_4_17·b_5_30 + b_2_42·b_1_25 + b_2_43·b_1_23 + b_2_4·b_1_24·a_3_4
       + b_2_42·b_1_22·a_3_4 + b_4_17·c_4_18·b_1_2 + b_2_4·c_4_19·b_3_10
       + b_2_4·c_4_19·b_1_23 + b_2_4·c_4_18·b_1_23 + b_2_42·c_4_19·b_1_2
       + b_2_42·c_4_18·b_1_2 + c_4_19·b_1_22·a_3_4 + c_4_18·b_1_22·a_3_4
       + b_4_16·c_4_19·a_1_0 + b_4_16·c_4_18·a_1_0 + b_2_4·c_4_19·a_3_4 + b_2_4·c_4_18·a_3_4
  60. b_4_16·b_5_30 + b_2_42·b_1_25 + b_2_4·b_1_24·a_3_4 + b_4_16·c_4_18·b_1_2
       + b_2_4·c_4_19·b_1_23 + b_2_4·c_4_18·b_1_23 + b_2_4·b_2_5·c_4_19·b_1_2
       + c_4_19·b_1_22·a_3_4 + c_4_18·b_1_22·a_3_4 + b_4_16·c_4_19·a_1_0
       + b_4_16·c_4_18·a_1_0 + b_2_5·c_4_19·a_3_4
  61. b_4_17·b_5_31 + b_2_5·b_1_1·b_1_2·b_5_31 + b_2_52·b_1_1·b_1_2·b_3_8
       + b_2_4·b_2_5·b_5_31 + b_2_42·b_5_31 + b_2_43·b_1_23 + b_2_44·b_1_2
       + b_2_42·b_1_22·a_3_4 + b_2_43·a_3_4 + b_4_17·c_4_18·b_1_2 + b_2_5·c_4_19·b_3_10
       + b_2_5·c_4_19·b_3_8 + b_2_5·c_4_18·b_3_8 + b_2_5·c_4_18·b_1_12·b_1_2
       + b_2_4·c_4_19·b_3_10 + b_2_4·c_4_18·b_3_10 + b_2_4·b_2_5·c_4_18·b_1_2
       + b_2_42·c_4_19·b_1_2 + b_2_4·c_4_19·a_3_4 + b_2_4·c_4_18·a_3_4
  62. b_4_16·b_5_31 + b_2_5·b_1_1·b_1_2·b_5_31 + b_2_42·b_5_31 + b_2_43·b_1_23
       + b_2_42·b_1_22·a_3_4 + b_4_16·c_4_18·b_1_2 + b_2_5·c_4_18·b_1_12·b_1_2
       + b_2_4·c_4_19·b_3_10 + b_2_4·b_2_5·c_4_19·b_1_2 + b_2_42·c_4_19·b_1_2
       + b_2_5·c_4_19·a_3_4 + b_2_4·c_4_19·a_3_4 + b_2_4·c_4_18·a_3_4
  63. b_5_302 + b_2_43·b_1_24 + b_2_43·b_4_17 + b_2_43·b_4_16 + b_2_44·b_2_5
       + b_2_42·c_4_19·b_1_22 + b_2_42·c_4_18·b_1_22 + b_2_42·b_2_5·c_4_19
       + c_4_182·b_1_22
  64. b_5_312 + b_2_52·b_1_15·b_1_2 + b_2_4·b_2_52·b_4_17 + b_2_42·b_2_5·b_4_17
       + b_2_43·b_4_17 + b_2_43·b_4_16 + b_2_45 + b_2_5·c_4_19·b_1_1·b_3_10
       + b_2_5·c_4_19·b_1_13·b_1_2 + b_2_53·c_4_19 + b_2_42·b_2_5·c_4_19
       + b_2_42·b_2_5·c_4_18 + c_4_18·c_4_19·b_1_12 + c_4_182·b_1_22 + c_4_182·b_1_12
  65. b_5_30·b_5_31 + b_2_44·b_1_22 + c_4_18·b_1_2·b_5_31 + c_4_18·b_1_2·b_5_30
       + b_2_4·b_2_52·c_4_19 + b_2_43·c_4_19 + b_2_43·c_4_18 + c_4_182·b_1_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 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_18, a Duflot regular element of degree 4
    2. c_4_19, a Duflot regular element of degree 4
    3. b_1_22 + b_1_1·b_1_2 + b_1_12 + b_2_5 + b_2_4, an element of degree 2
    4. b_3_9 + b_2_5·b_1_1 + b_2_4·b_1_2, an element of degree 3
  • The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 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. b_1_1 → 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. a_3_4 → 0, an element of degree 3
  7. b_3_8 → 0, an element of degree 3
  8. b_3_9 → 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. b_4_17 → 0, an element of degree 4
  12. c_4_18 → c_1_04, an element of degree 4
  13. c_4_19 → c_1_14, an element of degree 4
  14. b_5_30 → 0, an element of degree 5
  15. b_5_31 → 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. b_1_1 → c_1_2, 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 → c_1_32 + c_1_2·c_1_3, an element of degree 2
  6. a_3_4 → 0, an element of degree 3
  7. b_3_8 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_3_9 → 0, an element of degree 3
  9. b_3_10 → c_1_33 + c_1_22·c_1_3 + c_1_1·c_1_22 + c_1_12·c_1_2 + c_1_0·c_1_22 + c_1_02·c_1_2, an element of degree 3
  10. b_4_16 → 0, an element of degree 4
  11. b_4_17 → 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, an element of degree 4
  12. c_4_18 → 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_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
       + c_1_02·c_1_22 + c_1_04, an element of degree 4
  13. c_4_19 → c_1_12·c_1_22 + c_1_14, an element of degree 4
  14. b_5_30 → 0, an element of degree 5
  15. b_5_31 → c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32 + c_1_12·c_1_33
       + c_1_12·c_1_2·c_1_32 + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_23·c_1_3
       + c_1_0·c_1_1·c_1_23 + c_1_0·c_1_12·c_1_22 + 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_02·c_1_1·c_1_22
       + c_1_02·c_1_12·c_1_2 + c_1_04·c_1_2, 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. b_1_1 → c_1_3, an element of degree 1
  3. b_1_2 → c_1_3, an element of degree 1
  4. b_2_4 → 0, an element of degree 2
  5. b_2_5 → c_1_2·c_1_3 + c_1_22, an element of degree 2
  6. a_3_4 → 0, an element of degree 3
  7. b_3_8 → c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  8. b_3_9 → 0, an element of degree 3
  9. b_3_10 → c_1_2·c_1_32 + c_1_23 + c_1_1·c_1_32 + c_1_12·c_1_3 + c_1_0·c_1_32
       + c_1_02·c_1_3, an element of degree 3
  10. b_4_16 → c_1_2·c_1_33 + c_1_22·c_1_32, an element of degree 4
  11. b_4_17 → c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3
       + c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22, an element of degree 4
  12. c_4_18 → c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_1·c_1_2·c_1_32 + c_1_1·c_1_22·c_1_3
       + c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22 + 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 + c_1_02·c_1_22 + c_1_04, an element of degree 4
  13. c_4_19 → c_1_12·c_1_32 + c_1_14, an element of degree 4
  14. b_5_30 → c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_1·c_1_2·c_1_33 + c_1_1·c_1_22·c_1_32
       + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_3 + c_1_0·c_1_2·c_1_33
       + c_1_0·c_1_22·c_1_32 + c_1_02·c_1_33 + c_1_02·c_1_2·c_1_32
       + c_1_02·c_1_22·c_1_3 + c_1_04·c_1_3, an element of degree 5
  15. b_5_31 → c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_1·c_1_2·c_1_33 + c_1_1·c_1_23·c_1_3
       + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_23 + c_1_0·c_1_1·c_1_33
       + c_1_0·c_1_12·c_1_32 + c_1_02·c_1_1·c_1_32 + c_1_02·c_1_12·c_1_3, 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. b_1_1 → 0, an element of degree 1
  3. b_1_2 → c_1_3, an element of degree 1
  4. b_2_4 → c_1_2·c_1_3, an element of degree 2
  5. b_2_5 → c_1_22, an element of degree 2
  6. a_3_4 → 0, an element of degree 3
  7. b_3_8 → c_1_22·c_1_3, an element of degree 3
  8. b_3_9 → c_1_22·c_1_3, an element of degree 3
  9. b_3_10 → c_1_22·c_1_3 + c_1_23, an element of degree 3
  10. b_4_16 → c_1_34 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3 + c_1_0·c_1_2·c_1_32
       + c_1_02·c_1_32, an element of degree 4
  11. b_4_17 → c_1_34 + c_1_2·c_1_33 + c_1_12·c_1_32 + c_1_12·c_1_22 + 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
  12. c_4_18 → c_1_23·c_1_3 + c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22 + c_1_0·c_1_2·c_1_32
       + c_1_02·c_1_32 + c_1_02·c_1_22 + c_1_04, an element of degree 4
  13. c_4_19 → c_1_34 + c_1_2·c_1_33 + c_1_12·c_1_2·c_1_3 + c_1_14 + c_1_0·c_1_2·c_1_32
       + c_1_02·c_1_32, an element of degree 4
  14. b_5_30 → c_1_2·c_1_34 + c_1_0·c_1_2·c_1_33 + c_1_0·c_1_22·c_1_32 + c_1_02·c_1_33
       + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3 + c_1_04·c_1_3, an element of degree 5
  15. b_5_31 → c_1_22·c_1_33 + c_1_23·c_1_32 + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_23
       + c_1_0·c_1_2·c_1_33 + c_1_0·c_1_23·c_1_3 + c_1_02·c_1_33 + c_1_04·c_1_3, 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