Cohomology of group number 1561 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 4 minimal generators and exponent 4.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 3.
  • 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 coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t3  +  t  +  1) · (t4  −  3·t3  −  t  −  1)
    (t  +  1)2 · (t  −  1)4 · (t2  +  1)3
  • 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 16 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_1_3, an element of degree 1
  5. b_3_5, an element of degree 3
  6. b_3_6, an element of degree 3
  7. b_3_7, an element of degree 3
  8. b_3_8, an element of degree 3
  9. b_3_9, an element of degree 3
  10. b_3_10, an element of degree 3
  11. b_3_11, an element of degree 3
  12. c_4_19, a Duflot regular element of degree 4
  13. c_4_20, a Duflot regular element of degree 4
  14. c_4_21, a Duflot regular element of degree 4
  15. b_5_31, an element of degree 5
  16. b_5_32, 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 62 minimal relations of maximal degree 10:

  1. b_1_1·b_1_2 + a_1_02
  2. b_1_32 + b_1_2·b_1_3 + a_1_0·b_1_2 + a_1_0·b_1_1 + a_1_02
  3. b_1_1·b_1_3 + a_1_0·b_1_2
  4. a_1_02·b_1_1 + a_1_03
  5. a_1_0·b_1_12
  6. a_1_02·b_1_2 + a_1_03
  7. b_1_2·b_3_6 + a_1_0·b_3_5
  8. b_1_1·b_3_5 + a_1_0·b_3_6
  9. b_1_3·b_3_7 + b_1_3·b_3_6 + b_1_3·b_3_5 + b_1_2·b_3_8 + b_1_2·b_3_7 + a_1_0·b_3_8
  10. b_1_1·b_3_8 + a_1_0·b_3_7 + a_1_0·b_3_5
  11. b_1_3·b_3_7 + b_1_3·b_3_5 + b_1_2·b_3_8 + b_1_2·b_3_7 + a_1_0·b_3_9 + a_1_0·b_3_7
  12. b_1_1·b_3_9 + b_1_1·b_3_7 + a_1_0·b_3_7
  13. b_1_3·b_3_10 + b_1_3·b_3_8 + b_1_3·b_3_7 + b_1_2·b_3_10 + b_1_2·b_3_7 + b_1_2·b_3_5
       + b_1_1·b_3_5
  14. b_1_3·b_3_10 + b_1_3·b_3_9 + b_1_3·b_3_7 + b_1_3·b_3_6 + a_1_0·b_3_10 + a_1_0·b_3_7
  15. b_1_3·b_3_8 + b_1_3·b_3_6 + b_1_3·b_3_5 + b_1_1·b_3_10
  16. b_1_3·b_3_11 + b_1_3·b_3_9 + b_1_3·b_3_8 + b_1_3·b_3_7 + b_1_3·b_3_6 + b_1_3·b_3_5
       + b_1_2·b_3_8 + b_1_2·b_3_7 + b_1_1·b_3_5
  17. b_1_3·b_3_9 + b_1_3·b_3_8 + b_1_3·b_3_7 + b_1_2·b_3_11 + b_1_2·b_3_7 + b_1_1·b_3_5
       + a_1_0·b_3_7
  18. b_1_3·b_3_10 + b_1_3·b_3_9 + b_1_3·b_3_8 + b_1_2·b_3_8 + b_1_2·b_3_7 + a_1_0·b_3_11
       + a_1_0·b_3_7
  19. a_1_02·b_3_6 + a_1_02·b_3_5
  20. a_1_0·b_1_1·b_3_6 + a_1_02·b_3_7
  21. a_1_0·b_1_1·b_3_7 + a_1_0·b_1_1·b_3_6 + a_1_02·b_3_5
  22. b_3_8·b_3_11 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_9 + b_3_72
       + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_7
  23. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_11 + b_3_9·b_3_10 + b_3_82 + b_3_7·b_3_11
       + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_5·b_3_10 + b_3_5·b_3_9 + b_3_5·b_3_8
  24. b_3_10·b_3_11 + b_3_102 + b_3_92 + b_3_82 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_72
       + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_8 + b_1_23·b_3_11
       + b_1_23·b_3_10 + b_1_23·b_3_9 + c_4_19·b_1_22 + c_4_19·a_1_0·b_1_3
  25. b_3_10·b_3_11 + b_3_8·b_3_10 + b_3_7·b_3_10 + b_3_72 + b_3_6·b_3_9 + b_3_6·b_3_8
       + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_10 + b_3_5·b_3_7 + b_3_52 + b_1_23·b_3_11
       + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_7 + b_1_23·b_3_5 + b_1_13·b_3_11
       + b_1_13·b_3_6 + c_4_20·b_1_2·b_1_3 + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_12
       + c_4_19·a_1_0·b_1_3
  26. b_3_10·b_3_11 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_7·b_3_9 + b_3_72
       + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_8 + b_1_23·b_3_11
       + b_1_23·b_3_7 + c_4_19·b_1_2·b_1_3 + c_4_20·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_3
       + c_4_19·a_1_02
  27. b_3_10·b_3_11 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_72 + b_3_6·b_3_9
       + b_3_6·b_3_7 + b_3_5·b_3_9 + b_3_5·b_3_6 + b_3_52 + b_1_23·b_3_11 + b_1_23·b_3_10
       + b_1_23·b_3_9 + b_1_23·b_3_8 + b_1_13·b_3_11 + b_1_13·b_3_6 + c_4_20·b_1_22
       + c_4_19·b_1_12 + c_4_19·a_1_0·b_1_1
  28. b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_3_7·b_3_9 + b_3_72 + b_3_6·b_3_10
       + b_3_6·b_3_8 + b_3_5·b_3_9 + b_3_5·b_3_7 + b_3_52 + c_4_20·a_1_0·b_1_2
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_0·b_1_1
  29. b_3_10·b_3_11 + b_3_82 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_6·b_3_9
       + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_8 + b_1_23·b_3_11 + b_1_23·b_3_7
       + c_4_19·b_1_2·b_1_3 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_0·b_1_1
       + c_4_20·a_1_02
  30. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_7·b_3_10 + b_3_7·b_3_9 + b_3_72
       + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_10 + b_3_5·b_3_9
       + b_1_23·b_3_11 + b_1_23·b_3_7 + c_4_19·b_1_2·b_1_3 + c_4_20·a_1_0·b_1_1
       + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_0·b_1_1
  31. b_3_112 + b_3_10·b_3_11 + b_3_82 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_8 + b_1_13·b_3_7 + c_4_20·b_1_12
       + c_4_19·b_1_12 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_02
  32. b_3_102 + b_3_8·b_3_10 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_8
       + b_3_5·b_3_10 + b_3_5·b_3_8 + b_3_5·b_3_7 + b_3_5·b_3_6 + b_1_23·b_3_10 + b_1_23·b_3_7
       + b_1_23·b_3_5 + b_1_13·b_3_11 + b_1_13·b_3_6 + c_4_21·b_1_2·b_1_3
       + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_12 + c_4_19·a_1_0·b_1_1 + c_4_19·a_1_02
  33. b_3_10·b_3_11 + b_3_9·b_3_10 + b_3_7·b_3_10 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_72
       + b_3_6·b_3_8 + b_3_5·b_3_9 + b_3_5·b_3_6 + c_4_21·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_2
  34. b_3_10·b_3_11 + b_3_82 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_11 + b_3_5·b_3_8 + b_1_23·b_3_11 + b_1_13·b_3_11
       + b_1_13·b_3_6 + c_4_21·b_1_22 + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_12
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_0·b_1_1 + c_4_19·a_1_02
  35. b_3_10·b_3_11 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_3_7·b_3_10 + b_3_7·b_3_9
       + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_10
       + b_3_5·b_3_9 + b_3_5·b_3_6 + b_3_52 + c_4_21·a_1_0·b_1_2 + c_4_19·a_1_02
  36. b_3_10·b_3_11 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_6·b_3_9 + b_3_6·b_3_7
       + b_3_5·b_3_9 + b_3_5·b_3_6 + c_4_19·a_1_0·b_1_1 + c_4_21·a_1_02
  37. b_3_9·b_3_10 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_8
       + b_3_5·b_3_11 + b_3_5·b_3_9 + b_3_5·b_3_7 + b_1_23·b_3_11 + b_1_23·b_3_7
       + c_4_19·b_1_2·b_1_3 + c_4_21·a_1_0·b_1_1 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_1
       + c_4_19·a_1_02
  38. b_3_112 + b_3_10·b_3_11 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_72
       + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_62 + b_3_5·b_3_9 + b_3_5·b_3_6 + b_1_23·b_3_11
       + b_1_23·b_3_7 + b_1_13·b_3_7 + b_1_13·b_3_6 + c_4_21·b_1_12 + c_4_19·b_1_2·b_1_3
       + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_02
  39. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_3_7·b_3_10
       + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_6·b_3_10 + b_3_5·b_3_9 + b_3_5·b_3_8 + b_3_5·b_3_6
       + b_3_52 + b_1_3·b_5_31 + b_1_23·b_3_11 + b_1_23·b_3_10 + b_1_23·b_3_8 + b_1_23·b_3_7
       + b_1_23·b_3_5 + b_1_13·b_3_11 + b_1_13·b_3_6 + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_12
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_1
  40. b_3_92 + b_3_8·b_3_10 + b_3_7·b_3_8 + b_3_6·b_3_9 + b_3_6·b_3_8 + b_3_6·b_3_7
       + b_3_5·b_3_11 + b_3_5·b_3_10 + b_3_5·b_3_8 + b_3_5·b_3_6 + b_3_52 + b_1_2·b_5_31
       + b_1_23·b_3_11 + b_1_23·b_3_10 + b_1_23·b_3_7 + b_1_13·b_3_11 + b_1_13·b_3_6
       + c_4_19·b_1_2·b_1_3 + c_4_19·b_1_12 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_02
  41. b_3_102 + b_3_7·b_3_8 + b_3_6·b_3_8 + b_3_5·b_3_11 + b_3_5·b_3_10 + b_1_23·b_3_11
       + b_1_23·b_3_7 + a_1_0·b_5_31 + c_4_19·b_1_2·b_1_3 + c_4_19·a_1_0·b_1_3
       + c_4_19·a_1_0·b_1_1 + c_4_19·a_1_02
  42. b_3_112 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_7·b_3_9 + b_3_6·b_3_11 + b_3_6·b_3_10
       + b_3_6·b_3_9 + b_3_62 + b_3_5·b_3_11 + b_3_5·b_3_10 + b_3_5·b_3_9 + b_3_5·b_3_8
       + b_3_5·b_3_6 + b_3_52 + b_1_1·b_5_31 + c_4_19·b_1_12 + c_4_19·a_1_0·b_1_3
       + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_0·b_1_1
  43. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_9 + b_3_82 + b_3_7·b_3_10
       + b_3_7·b_3_8 + b_3_72 + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_8 + b_3_6·b_3_7
       + b_3_5·b_3_11 + b_3_5·b_3_9 + b_3_5·b_3_8 + b_3_52 + b_1_3·b_5_32 + b_1_23·b_3_10
       + b_1_23·b_3_8 + b_1_23·b_3_5 + b_1_13·b_3_11 + b_1_13·b_3_6 + c_4_19·b_1_12
  44. b_3_10·b_3_11 + b_3_102 + b_3_9·b_3_10 + b_3_82 + b_3_7·b_3_10 + b_3_7·b_3_8 + b_3_72
       + b_3_6·b_3_9 + b_3_6·b_3_7 + b_3_5·b_3_10 + b_3_5·b_3_8 + b_3_5·b_3_7 + b_1_2·b_5_32
       + b_1_23·b_3_11 + b_1_23·b_3_7 + b_1_23·b_3_5 + b_1_13·b_3_11 + b_1_13·b_3_6
       + c_4_19·b_1_12 + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_0·b_1_1
  45. b_3_8·b_3_10 + b_3_8·b_3_9 + b_3_7·b_3_10 + b_3_7·b_3_9 + b_3_7·b_3_8 + b_3_72
       + b_3_6·b_3_10 + b_3_6·b_3_9 + b_3_6·b_3_8 + b_3_6·b_3_7 + a_1_0·b_5_32
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_1 + c_4_19·a_1_02
  46. b_3_10·b_3_11 + b_3_8·b_3_10 + b_3_82 + b_3_7·b_3_10 + b_3_6·b_3_11 + b_3_6·b_3_10
       + b_3_6·b_3_8 + b_3_5·b_3_11 + b_3_5·b_3_10 + b_3_5·b_3_7 + b_3_5·b_3_6 + b_3_52
       + b_1_23·b_3_11 + b_1_23·b_3_7 + b_1_1·b_5_32 + b_1_13·b_3_6 + c_4_19·b_1_2·b_1_3
       + c_4_19·a_1_0·b_1_3 + c_4_19·a_1_0·b_1_2 + c_4_19·a_1_02
  47. a_1_0·b_1_1·b_5_32 + a_1_0·b_1_1·b_5_31 + c_4_20·a_1_03
  48. b_3_10·b_5_31 + b_3_5·b_5_31 + b_1_22·b_3_5·b_3_8 + b_1_23·b_5_31 + b_1_25·b_3_10
       + b_1_25·b_3_7 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_7
       + c_4_21·b_1_2·b_3_5 + c_4_21·b_1_23·b_1_3 + c_4_20·b_1_2·b_3_10 + c_4_20·b_1_2·b_3_5
       + c_4_20·b_1_23·b_1_3 + c_4_20·b_1_24 + c_4_19·b_1_2·b_3_8 + c_4_19·b_1_23·b_1_3
       + c_4_19·b_1_24 + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8
       + c_4_20·a_1_0·b_3_11 + c_4_20·a_1_0·b_3_9 + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_6
       + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_8
       + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6 + c_4_19·a_1_0·b_3_5
  49. b_3_11·b_5_31 + b_3_7·b_5_31 + b_3_6·b_5_31 + b_1_23·b_5_31 + b_1_25·b_3_8
       + b_1_25·b_3_5 + b_1_12·b_3_7·b_3_11 + b_1_15·b_3_11 + c_4_21·b_1_23·b_1_3
       + c_4_21·b_1_24 + c_4_21·b_1_1·b_3_6 + c_4_21·b_1_14 + c_4_20·b_1_2·b_3_11
       + c_4_20·b_1_2·b_3_7 + c_4_20·b_1_24 + c_4_20·b_1_1·b_3_11 + c_4_20·b_1_1·b_3_7
       + c_4_20·b_1_1·b_3_6 + c_4_20·b_1_14 + c_4_19·b_1_2·b_3_11 + c_4_19·b_1_2·b_3_10
       + c_4_19·b_1_2·b_3_8 + c_4_19·b_1_2·b_3_7 + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_23·b_1_3
       + c_4_19·b_1_24 + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_7
       + c_4_21·a_1_0·b_3_5 + c_4_20·a_1_0·b_3_11 + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_6
       + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6
       + c_4_19·a_1_0·b_3_5
  50. b_3_10·b_5_31 + b_3_8·b_5_31 + b_1_22·b_3_5·b_3_8 + b_1_23·b_5_31 + b_1_25·b_3_11
       + b_1_25·b_3_10 + b_1_25·b_3_9 + b_1_25·b_3_7 + b_1_25·b_3_5 + c_4_21·b_1_2·b_3_11
       + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_7 + c_4_21·b_1_23·b_1_3
       + c_4_20·b_1_2·b_3_10 + c_4_20·b_1_2·b_3_8 + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_23·b_1_3
       + c_4_19·b_1_24 + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_6 + c_4_21·a_1_0·b_3_5
       + c_4_20·a_1_0·b_3_8 + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_6 + c_4_19·a_1_0·b_3_11
       + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6 + c_4_19·a_1_0·b_3_5
  51. b_3_11·b_5_31 + b_3_9·b_5_31 + b_3_6·b_5_31 + b_1_22·b_3_5·b_3_8 + b_1_22·b_3_5·b_3_7
       + b_1_23·b_5_32 + b_1_23·b_5_31 + b_1_25·b_3_11 + b_1_25·b_3_8 + b_1_12·b_3_7·b_3_11
       + b_1_15·b_3_11 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_9
       + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_5 + c_4_21·b_1_23·b_1_3 + c_4_21·b_1_1·b_3_6
       + c_4_21·b_1_14 + c_4_20·b_1_2·b_3_9 + c_4_20·b_1_2·b_3_7 + c_4_20·b_1_24
       + c_4_20·b_1_1·b_3_11 + c_4_20·b_1_1·b_3_7 + c_4_20·b_1_1·b_3_6 + c_4_20·b_1_14
       + c_4_19·b_1_2·b_3_10 + c_4_19·b_1_2·b_3_9 + c_4_19·b_1_2·b_3_8 + c_4_19·b_1_2·b_3_7
       + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_23·b_1_3 + c_4_19·b_1_24 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6 + c_4_21·a_1_0·b_3_5 + c_4_20·a_1_0·b_3_11
       + c_4_20·a_1_0·b_3_9 + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_6 + c_4_19·a_1_0·b_3_10
       + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_8 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6
       + c_4_19·a_1_0·b_3_5
  52. b_3_10·b_5_31 + b_1_22·b_3_5·b_3_8 + b_1_22·b_3_5·b_3_7 + b_1_22·b_1_3·b_5_32
       + b_1_25·b_3_9 + b_1_25·b_3_8 + b_1_25·b_3_5 + a_1_03·b_5_31 + c_4_21·b_1_2·b_3_11
       + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_2·b_3_7 + c_4_21·b_1_2·b_3_5 + c_4_21·b_1_23·b_1_3
       + c_4_20·b_1_2·b_3_11 + c_4_20·b_1_2·b_3_10 + c_4_20·b_1_2·b_3_7 + c_4_20·b_1_23·b_1_3
       + c_4_20·b_1_24 + c_4_19·b_1_2·b_3_11 + c_4_19·b_1_2·b_3_10 + c_4_19·b_1_2·b_3_7
       + c_4_21·a_1_0·b_3_7 + c_4_21·a_1_0·b_3_6 + c_4_20·a_1_0·b_3_9 + c_4_20·a_1_0·b_3_6
       + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_11 + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_9
       + c_4_19·a_1_0·b_3_8
  53. b_3_6·b_5_31 + b_1_13·b_5_32 + a_1_03·b_5_31 + c_4_21·b_1_1·b_3_11
       + c_4_21·b_1_1·b_3_7 + c_4_21·b_1_1·b_3_6 + c_4_21·b_1_14 + c_4_20·b_1_1·b_3_11
       + c_4_20·b_1_1·b_3_7 + c_4_20·b_1_14 + c_4_19·b_1_1·b_3_11 + c_4_19·b_1_1·b_3_7
       + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_14 + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_5 + c_4_20·a_1_0·b_3_11 + c_4_20·a_1_0·b_3_7
       + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_11 + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_8
       + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_6
  54. b_3_10·b_5_32 + b_1_22·b_3_5·b_3_9 + b_1_22·b_3_5·b_3_8 + b_1_25·b_3_9
       + b_1_25·b_3_5 + a_1_03·b_5_31 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_10
       + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_23·b_1_3 + c_4_20·b_1_2·b_3_11 + c_4_20·b_1_2·b_3_10
       + c_4_20·b_1_2·b_3_9 + c_4_20·b_1_2·b_3_7 + c_4_20·b_1_2·b_3_5 + c_4_19·b_1_2·b_3_11
       + c_4_19·b_1_2·b_3_8 + c_4_19·b_1_24 + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_9
       + c_4_20·a_1_0·b_3_10 + c_4_20·a_1_0·b_3_6 + c_4_19·a_1_0·b_3_11 + c_4_19·a_1_0·b_3_9
  55. b_3_11·b_5_32 + b_3_6·b_5_31 + b_3_5·b_5_32 + b_1_22·b_3_5·b_3_9 + b_1_22·b_3_5·b_3_7
       + b_1_25·b_3_11 + b_1_25·b_3_9 + b_1_25·b_3_8 + b_1_25·b_3_5 + b_1_13·b_5_31
       + b_1_15·b_3_7 + b_1_15·b_3_6 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_5
       + c_4_21·b_1_1·b_3_11 + c_4_21·b_1_1·b_3_7 + c_4_21·b_1_1·b_3_6 + c_4_21·b_1_14
       + c_4_20·b_1_2·b_3_9 + c_4_20·b_1_2·b_3_7 + c_4_20·b_1_23·b_1_3 + c_4_20·b_1_1·b_3_11
       + c_4_20·b_1_1·b_3_7 + c_4_20·b_1_1·b_3_6 + c_4_19·b_1_2·b_3_10 + c_4_19·b_1_2·b_3_8
       + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_24 + c_4_19·b_1_1·b_3_11 + c_4_19·b_1_1·b_3_7
       + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_14 + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_9
       + c_4_20·a_1_0·b_3_9 + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_6 + c_4_20·a_1_0·b_3_5
       + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_9 + c_4_19·a_1_0·b_3_8 + c_4_19·a_1_0·b_3_5
  56. b_3_6·b_5_32 + b_3_6·b_5_31 + c_4_21·b_1_1·b_3_7 + c_4_21·b_1_1·b_3_6
       + c_4_20·b_1_1·b_3_7 + c_4_19·b_1_1·b_3_7 + c_4_19·b_1_1·b_3_6 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_3_7 + c_4_21·a_1_0·b_3_6 + c_4_21·a_1_0·b_3_5 + c_4_20·a_1_0·b_3_9
       + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_5
  57. b_3_11·b_5_32 + b_3_11·b_5_31 + b_3_10·b_5_31 + b_3_7·b_5_32 + b_3_6·b_5_31
       + b_1_22·b_3_5·b_3_8 + b_1_23·b_5_31 + b_1_25·b_3_11 + b_1_25·b_3_10 + b_1_25·b_3_9
       + b_1_25·b_3_7 + b_1_25·b_3_5 + b_1_12·b_3_7·b_3_11 + b_1_13·b_5_31 + b_1_15·b_3_7
       + c_4_21·b_1_2·b_3_10 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_23·b_1_3 + c_4_21·b_1_1·b_3_7
       + c_4_21·b_1_1·b_3_6 + c_4_20·b_1_2·b_3_11 + c_4_20·b_1_2·b_3_10 + c_4_20·b_1_1·b_3_11
       + c_4_20·b_1_1·b_3_7 + c_4_20·b_1_14 + c_4_19·b_1_2·b_3_11 + c_4_19·b_1_2·b_3_8
       + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_23·b_1_3 + c_4_19·b_1_24 + c_4_19·b_1_1·b_3_7
       + c_4_19·b_1_1·b_3_6 + c_4_21·a_1_0·b_3_10 + c_4_21·a_1_0·b_3_8 + c_4_21·a_1_0·b_3_6
       + c_4_21·a_1_0·b_3_5 + c_4_20·a_1_0·b_3_11 + c_4_20·a_1_0·b_3_7 + c_4_20·a_1_0·b_3_6
       + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_11 + c_4_19·a_1_0·b_3_10 + c_4_19·a_1_0·b_3_9
       + c_4_19·a_1_0·b_3_8
  58. b_3_11·b_5_32 + b_3_8·b_5_32 + b_3_6·b_5_31 + b_1_23·b_5_31 + b_1_25·b_3_10
       + b_1_25·b_3_8 + b_1_25·b_3_7 + b_1_13·b_5_31 + b_1_15·b_3_7 + b_1_15·b_3_6
       + a_1_03·b_5_31 + c_4_21·b_1_2·b_3_11 + c_4_21·b_1_2·b_3_8 + c_4_21·b_1_24
       + c_4_21·b_1_1·b_3_11 + c_4_21·b_1_1·b_3_7 + c_4_21·b_1_1·b_3_6 + c_4_21·b_1_14
       + c_4_20·b_1_2·b_3_10 + c_4_20·b_1_2·b_3_8 + c_4_20·b_1_2·b_3_5 + c_4_20·b_1_24
       + c_4_20·b_1_1·b_3_11 + c_4_20·b_1_1·b_3_7 + c_4_20·b_1_1·b_3_6 + c_4_19·b_1_2·b_3_10
       + c_4_19·b_1_2·b_3_8 + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_24 + c_4_19·b_1_1·b_3_11
       + c_4_19·b_1_1·b_3_7 + c_4_19·b_1_1·b_3_6 + c_4_19·b_1_14 + c_4_21·a_1_0·b_3_9
       + c_4_21·a_1_0·b_3_5 + c_4_20·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_11 + c_4_19·a_1_0·b_3_9
       + c_4_19·a_1_0·b_3_8
  59. b_3_11·b_5_32 + b_3_9·b_5_32 + b_3_9·b_5_31 + b_1_22·b_3_5·b_3_8 + b_1_22·b_3_5·b_3_7
       + b_1_23·b_5_31 + b_1_25·b_3_11 + b_1_25·b_3_10 + b_1_25·b_3_7 + b_1_13·b_5_31
       + b_1_15·b_3_11 + b_1_15·b_3_7 + a_1_03·b_5_31 + c_4_21·b_1_2·b_3_11
       + c_4_21·b_1_23·b_1_3 + c_4_21·b_1_24 + c_4_21·b_1_1·b_3_7 + c_4_21·b_1_14
       + c_4_20·b_1_2·b_3_11 + c_4_20·b_1_2·b_3_9 + c_4_20·b_1_2·b_3_5 + c_4_20·b_1_23·b_1_3
       + c_4_20·b_1_24 + c_4_20·b_1_1·b_3_6 + c_4_19·b_1_2·b_3_11 + c_4_19·b_1_2·b_3_9
       + c_4_19·b_1_2·b_3_5 + c_4_19·b_1_24 + c_4_19·b_1_1·b_3_7 + c_4_19·b_1_1·b_3_6
       + c_4_21·a_1_0·b_3_11 + c_4_21·a_1_0·b_3_9 + c_4_21·a_1_0·b_3_6 + c_4_20·a_1_0·b_3_7
       + c_4_20·a_1_0·b_3_6 + c_4_20·a_1_0·b_3_5 + c_4_19·a_1_0·b_3_7 + c_4_19·a_1_0·b_3_5
  60. b_5_322 + b_1_24·b_3_5·b_3_9 + b_1_24·b_1_3·b_5_32 + b_1_25·b_5_32 + b_1_25·b_5_31
       + b_1_27·b_3_10 + b_1_27·b_3_9 + b_1_27·b_3_8 + b_1_27·b_3_7 + b_1_15·b_5_31
       + b_1_17·b_3_7 + b_1_17·b_3_6 + c_4_21·b_1_23·b_3_11 + c_4_21·b_1_23·b_3_10
       + c_4_21·b_1_23·b_3_8 + c_4_21·b_1_23·b_3_7 + c_4_21·b_1_23·b_3_5
       + c_4_21·b_1_13·b_3_11 + c_4_21·b_1_13·b_3_7 + c_4_21·b_1_13·b_3_6 + c_4_21·b_1_16
       + c_4_20·b_1_23·b_3_11 + c_4_20·b_1_23·b_3_9 + c_4_20·b_1_23·b_3_7
       + c_4_20·b_1_23·b_3_5 + c_4_20·b_1_13·b_3_11 + c_4_20·b_1_13·b_3_7
       + c_4_19·b_1_23·b_3_10 + c_4_19·b_1_23·b_3_9 + c_4_19·b_1_26
       + c_4_19·b_1_13·b_3_11 + c_4_19·b_1_13·b_3_7 + c_4_19·b_1_13·b_3_6 + c_4_19·b_1_16
       + c_4_212·b_1_22 + c_4_20·c_4_21·b_1_2·b_1_3 + c_4_20·c_4_21·b_1_12
       + c_4_202·b_1_22 + c_4_202·b_1_12 + c_4_19·c_4_21·b_1_2·b_1_3
       + c_4_19·c_4_20·b_1_2·b_1_3 + c_4_19·c_4_20·b_1_22 + c_4_19·c_4_20·b_1_12
       + c_4_192·b_1_2·b_1_3 + c_4_20·c_4_21·a_1_0·b_1_2 + c_4_20·c_4_21·a_1_0·b_1_1
       + c_4_19·c_4_21·a_1_0·b_1_2 + c_4_19·c_4_21·a_1_0·b_1_1 + c_4_19·c_4_20·a_1_0·b_1_2
       + c_4_19·c_4_20·a_1_0·b_1_1 + c_4_192·a_1_0·b_1_2 + c_4_192·a_1_0·b_1_1
       + c_4_212·a_1_02 + c_4_20·c_4_21·a_1_02 + c_4_19·c_4_21·a_1_02
  61. b_5_322 + b_5_312 + b_1_24·b_3_5·b_3_9 + b_1_24·b_3_5·b_3_8 + b_1_24·b_3_5·b_3_7
       + b_1_25·b_5_32 + b_1_27·b_3_10 + b_1_27·b_3_8 + b_1_27·b_3_7 + b_1_15·b_5_32
       + b_1_17·b_3_11 + b_1_17·b_3_6 + c_4_21·b_1_23·b_3_10 + c_4_21·b_1_23·b_3_8
       + c_4_21·b_1_23·b_3_5 + c_4_21·b_1_26 + c_4_21·b_1_13·b_3_11 + c_4_21·b_1_13·b_3_6
       + c_4_21·b_1_16 + c_4_20·b_1_23·b_3_9 + c_4_20·b_1_23·b_3_5 + c_4_20·b_1_25·b_1_3
       + c_4_20·b_1_13·b_3_11 + c_4_20·b_1_13·b_3_6 + c_4_20·b_1_16
       + c_4_19·b_1_23·b_3_11 + c_4_19·b_1_23·b_3_10 + c_4_19·b_1_23·b_3_9
       + c_4_19·b_1_23·b_3_8 + c_4_19·b_1_25·b_1_3 + c_4_19·b_1_13·b_3_11
       + c_4_212·b_1_2·b_1_3 + c_4_212·b_1_12 + c_4_20·c_4_21·b_1_2·b_1_3
       + c_4_19·c_4_21·b_1_12 + c_4_19·c_4_20·b_1_22 + c_4_19·c_4_20·b_1_12
       + c_4_192·b_1_22 + c_4_212·a_1_0·b_1_2 + c_4_212·a_1_0·b_1_1
       + c_4_20·c_4_21·a_1_0·b_1_2 + c_4_20·c_4_21·a_1_0·b_1_1 + c_4_202·a_1_02
       + c_4_19·c_4_20·a_1_02 + c_4_192·a_1_02
  62. b_5_31·b_5_32 + b_1_24·b_3_5·b_3_9 + b_1_24·b_3_5·b_3_7 + b_1_27·b_3_11
       + b_1_27·b_3_10 + b_1_27·b_3_9 + b_1_27·b_3_8 + b_1_27·b_3_7 + b_1_15·b_5_31
       + b_1_17·b_3_7 + b_1_17·b_3_6 + c_4_21·b_3_7·b_3_11 + c_4_21·b_1_3·b_5_32
       + c_4_21·b_1_2·b_5_32 + c_4_21·b_1_23·b_3_11 + c_4_21·b_1_23·b_3_8
       + c_4_21·b_1_23·b_3_5 + c_4_21·b_1_25·b_1_3 + c_4_21·b_1_1·b_5_32
       + c_4_21·b_1_13·b_3_11 + c_4_21·b_1_13·b_3_6 + c_4_21·b_1_16 + c_4_20·b_3_7·b_3_11
       + c_4_20·b_1_2·b_5_32 + c_4_20·b_1_2·b_5_31 + c_4_20·b_1_23·b_3_10
       + c_4_20·b_1_23·b_3_9 + c_4_20·b_1_25·b_1_3 + c_4_20·b_1_13·b_3_11
       + c_4_19·b_3_7·b_3_11 + c_4_19·b_1_2·b_5_32 + c_4_19·b_1_2·b_5_31
       + c_4_19·b_1_23·b_3_11 + c_4_19·b_1_23·b_3_7 + c_4_19·b_1_23·b_3_5
       + c_4_19·b_1_25·b_1_3 + c_4_19·b_1_26 + c_4_19·b_1_1·b_5_32 + c_4_19·b_1_13·b_3_11
       + c_4_19·b_1_13·b_3_6 + c_4_19·b_1_16 + c_4_21·a_1_0·b_5_31 + c_4_20·a_1_0·b_5_32
       + c_4_20·a_1_0·b_5_31 + c_4_19·a_1_0·b_5_31 + c_4_212·b_1_22
       + c_4_20·c_4_21·b_1_2·b_1_3 + c_4_20·c_4_21·b_1_12 + c_4_202·b_1_22
       + c_4_202·b_1_12 + c_4_19·c_4_21·b_1_2·b_1_3 + c_4_19·c_4_20·b_1_12
       + c_4_192·b_1_22 + c_4_212·a_1_0·b_1_3 + c_4_212·a_1_0·b_1_2
       + c_4_212·a_1_0·b_1_1 + c_4_20·c_4_21·a_1_0·b_1_2 + c_4_20·c_4_21·a_1_0·b_1_1
       + c_4_19·c_4_21·a_1_0·b_1_2 + c_4_19·c_4_20·a_1_0·b_1_3 + c_4_19·c_4_20·a_1_0·b_1_1
       + c_4_192·a_1_0·b_1_3 + c_4_192·a_1_0·b_1_1 + c_4_20·c_4_21·a_1_02
       + c_4_202·a_1_02 + c_4_19·c_4_20·a_1_02

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_19, a Duflot regular element of degree 4
    2. c_4_20, a Duflot regular element of degree 4
    3. c_4_21, a Duflot regular element of degree 4
    4. b_1_22 + b_1_12, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 8, 10].
  • 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 3

  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_1_3 → 0, an element of degree 1
  5. b_3_5 → 0, an element of degree 3
  6. b_3_6 → 0, an element of degree 3
  7. b_3_7 → 0, an element of degree 3
  8. b_3_8 → 0, an element of degree 3
  9. b_3_9 → 0, an element of degree 3
  10. b_3_10 → 0, an element of degree 3
  11. b_3_11 → 0, an element of degree 3
  12. c_4_19 → c_1_24, an element of degree 4
  13. c_4_20 → c_1_24 + c_1_14, an element of degree 4
  14. c_4_21 → c_1_14 + c_1_04, an element of degree 4
  15. b_5_31 → 0, an element of degree 5
  16. b_5_32 → 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_3, an element of degree 1
  3. b_1_2 → 0, an element of degree 1
  4. b_1_3 → 0, an element of degree 1
  5. b_3_5 → 0, an element of degree 3
  6. b_3_6 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  7. b_3_7 → c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  8. b_3_8 → 0, an element of degree 3
  9. b_3_9 → c_1_2·c_1_32 + c_1_22·c_1_3, an element of degree 3
  10. b_3_10 → 0, an element of degree 3
  11. b_3_11 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  12. c_4_19 → c_1_2·c_1_33 + c_1_24 + c_1_1·c_1_33 + c_1_12·c_1_32 + c_1_0·c_1_33
       + c_1_02·c_1_32, an element of degree 4
  13. c_4_20 → c_1_22·c_1_32 + c_1_24 + c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33
       + c_1_02·c_1_32, an element of degree 4
  14. c_4_21 → c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_12·c_1_32 + c_1_14 + c_1_0·c_1_33
       + c_1_04, an element of degree 4
  15. b_5_31 → c_1_2·c_1_34 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_14·c_1_3 + c_1_0·c_1_34
       + 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 + c_1_04·c_1_3, an element of degree 5
  16. b_5_32 → c_1_0·c_1_34 + c_1_0·c_1_2·c_1_33 + c_1_0·c_1_22·c_1_32 + c_1_0·c_1_1·c_1_33
       + c_1_0·c_1_12·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_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_1_3 → 0, an element of degree 1
  5. b_3_5 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  6. b_3_6 → 0, an element of degree 3
  7. b_3_7 → 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
  8. b_3_8 → 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
  9. b_3_9 → c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  10. b_3_10 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  11. b_3_11 → 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
  12. c_4_19 → c_1_2·c_1_33 + c_1_24, an element of degree 4
  13. c_4_20 → c_1_2·c_1_33 + c_1_24 + c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_02·c_1_32, an element of degree 4
  14. c_4_21 → c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_04, an element of degree 4
  15. b_5_31 → c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_1·c_1_34 + c_1_12·c_1_33 + c_1_02·c_1_33
       + c_1_04·c_1_3, an element of degree 5
  16. b_5_32 → 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_34 + c_1_04·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_1_3 → c_1_3, an element of degree 1
  5. b_3_5 → c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  6. b_3_6 → 0, an element of degree 3
  7. b_3_7 → c_1_33 + 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
  8. b_3_8 → c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  9. b_3_9 → c_1_1·c_1_32 + c_1_12·c_1_3, an element of degree 3
  10. b_3_10 → c_1_33 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
  11. b_3_11 → c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + 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
  12. c_4_19 → c_1_2·c_1_33 + c_1_24, an element of degree 4
  13. c_4_20 → c_1_34 + c_1_22·c_1_32 + c_1_24 + c_1_12·c_1_32 + c_1_14 + c_1_0·c_1_33
       + c_1_02·c_1_32, an element of degree 4
  14. c_4_21 → c_1_1·c_1_33 + c_1_14 + c_1_0·c_1_33 + c_1_04, an element of degree 4
  15. b_5_31 → c_1_35 + c_1_2·c_1_34 + c_1_22·c_1_33 + c_1_12·c_1_33 + c_1_14·c_1_3
       + c_1_0·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, an element of degree 5
  16. b_5_32 → c_1_1·c_1_34 + c_1_14·c_1_3 + c_1_0·c_1_34 + 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
       + 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