Cohomology of group number 860 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 4.
  • It is non-abelian.
  • It has p-Rank 4.
  • Its center has rank 1.
  • It has 3 conjugacy classes of maximal elementary abelian subgroups, which are of rank 3, 3 and 4, respectively.

Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 4 and depth 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    t5  −  t4  +  t2  −  t  +  1
    (t  −  1)4 · (t2  +  1) · (t4  +  1)
  • 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 14 minimal generators of maximal degree 8:

  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. b_3_8, an element of degree 3
  7. b_3_9, an element of degree 3
  8. b_3_10, an element of degree 3
  9. b_4_16, an element of degree 4
  10. b_5_21, an element of degree 5
  11. b_5_23, an element of degree 5
  12. b_6_32, an element of degree 6
  13. b_7_42, an element of degree 7
  14. c_8_57, a Duflot regular element of degree 8

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

Ring relations

There are 51 minimal relations of maximal degree 14:

  1. a_1_02
  2. a_1_0·b_1_1
  3. a_1_0·b_1_22
  4. b_2_4·b_1_1 + b_2_5·a_1_0
  5. b_2_5·b_1_1 + b_2_4·b_1_1
  6. b_2_52 + b_2_4·b_1_22 + b_2_4·b_2_5 + b_2_5·a_1_0·b_1_2
  7. a_1_0·b_3_8
  8. b_2_4·b_1_22 + a_1_0·b_3_9 + b_2_5·a_1_0·b_1_2
  9. b_1_1·b_3_9 + b_1_1·b_3_8 + b_2_5·b_1_22 + b_2_5·a_1_0·b_1_2
  10. b_2_5·b_1_22 + a_1_0·b_3_10
  11. b_2_5·b_3_8
  12. b_2_4·b_3_8
  13. b_1_22·b_3_9 + b_1_22·b_3_8 + b_2_5·b_3_10 + b_2_5·b_3_9 + b_2_4·b_2_5·b_1_2
       + a_1_0·b_1_2·b_3_9
  14. b_1_22·b_3_9 + b_1_22·b_3_8 + a_1_0·b_1_2·b_3_10
  15. b_2_5·b_3_9 + b_2_4·b_3_10 + b_2_4·b_2_5·b_1_2 + a_1_0·b_1_2·b_3_9
  16. a_1_0·b_1_2·b_3_9 + b_4_16·a_1_0
  17. b_3_8·b_3_9 + b_3_82
  18. b_3_9·b_3_10 + b_3_8·b_3_10 + b_2_5·b_4_16 + b_2_4·a_1_0·b_3_10
  19. b_3_92 + b_3_82 + b_2_4·b_1_2·b_3_9 + b_2_4·b_4_16 + b_2_4·a_1_0·b_3_9
       + b_2_4·b_2_5·a_1_0·b_1_2
  20. b_3_82 + b_1_26 + b_1_1·b_1_22·b_3_8 + b_1_1·b_1_25 + b_1_12·b_1_2·b_3_8
       + b_1_12·b_1_24 + b_1_13·b_3_10 + b_1_13·b_3_8 + b_1_14·b_1_22 + b_4_16·b_1_12
  21. a_1_0·b_5_21
  22. b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_1_26 + b_1_1·b_5_21
       + b_1_1·b_1_22·b_3_10 + b_1_12·b_1_2·b_3_10 + b_1_13·b_3_10 + b_1_14·b_1_22
       + b_4_16·b_1_22 + b_4_16·b_1_1·b_1_2 + b_2_4·b_1_2·b_3_10
  23. a_1_0·b_5_23 + b_2_4·a_1_0·b_3_10 + b_2_4·b_2_5·a_1_0·b_1_2
  24. b_3_102 + b_3_9·b_3_10 + b_3_8·b_3_10 + b_3_82 + b_1_26 + b_1_1·b_5_23
       + b_1_1·b_1_22·b_3_10 + b_1_1·b_1_22·b_3_8 + b_1_1·b_1_25 + b_1_12·b_1_2·b_3_8
       + b_1_14·b_1_22 + b_4_16·b_1_22 + b_2_4·b_1_2·b_3_10 + b_2_4·a_1_0·b_3_10
       + b_2_4·b_2_5·a_1_0·b_1_2
  25. b_2_5·b_5_21 + b_2_4·b_5_21
  26. b_2_5·b_5_23 + b_2_5·b_4_16·b_1_2 + b_2_42·b_3_10 + b_2_42·b_2_5·b_1_2
       + b_2_4·a_1_0·b_1_2·b_3_10 + b_2_4·b_4_16·a_1_0 + b_2_42·b_2_5·a_1_0
  27. b_1_22·b_5_23 + b_1_22·b_5_21 + b_1_24·b_3_8 + b_1_27 + b_1_1·b_1_23·b_3_10
       + b_1_1·b_1_23·b_3_8 + b_1_12·b_1_22·b_3_10 + b_4_16·b_1_23
       + b_2_4·a_1_0·b_1_2·b_3_10
  28. b_6_32·a_1_0 + b_2_4·b_4_16·a_1_0 + b_2_42·b_2_5·a_1_0
  29. b_1_22·b_5_21 + b_1_24·b_3_10 + b_1_1·b_3_8·b_3_10 + b_1_1·b_1_2·b_5_21
       + b_1_1·b_1_26 + b_1_12·b_5_21 + b_1_12·b_1_25 + b_1_13·b_1_2·b_3_10
       + b_1_13·b_1_2·b_3_8 + b_1_14·b_3_10 + b_6_32·b_1_1 + b_4_16·b_3_8
       + b_4_16·b_1_12·b_1_2 + b_4_16·b_1_13 + b_2_4·a_1_0·b_1_2·b_3_10
       + b_2_42·b_2_5·a_1_0
  30. b_3_10·b_5_23 + b_3_10·b_5_21 + b_3_9·b_5_21 + b_3_8·b_5_21 + b_1_22·b_3_8·b_3_10
       + b_1_25·b_3_10 + b_1_1·b_1_2·b_3_8·b_3_10 + b_1_12·b_1_2·b_5_21
       + b_1_12·b_1_23·b_3_10 + b_1_12·b_1_23·b_3_8 + b_1_12·b_1_26 + b_1_13·b_5_21
       + b_1_14·b_1_2·b_3_10 + b_1_14·b_1_24 + b_1_15·b_3_8 + b_4_16·b_1_2·b_3_10
       + b_4_16·b_1_1·b_1_23 + b_4_16·b_1_14 + b_2_4·b_1_2·b_5_21 + b_2_4·b_2_5·b_4_16
  31. b_3_8·b_5_23 + b_3_8·b_5_21 + b_1_25·b_3_8 + b_1_28 + b_1_1·b_1_2·b_3_8·b_3_10
       + b_1_1·b_1_24·b_3_8 + b_1_12·b_3_8·b_3_10 + b_1_13·b_1_22·b_3_10
       + b_1_13·b_1_25 + b_1_14·b_1_2·b_3_10 + b_1_14·b_1_2·b_3_8 + b_1_14·b_1_24
       + b_1_15·b_1_23 + b_4_16·b_1_2·b_3_8 + b_4_16·b_1_12·b_1_22
       + b_4_16·b_1_13·b_1_2
  32. b_3_9·b_5_21 + b_3_8·b_5_21 + b_2_5·b_6_32 + b_2_4·b_2_5·b_4_16 + b_2_43·b_2_5
       + b_2_42·a_1_0·b_3_10 + b_2_42·a_1_0·b_3_9
  33. b_3_9·b_5_23 + b_3_9·b_5_21 + b_1_25·b_3_8 + b_1_28 + b_1_1·b_1_2·b_3_8·b_3_10
       + b_1_1·b_1_24·b_3_8 + b_1_12·b_3_8·b_3_10 + b_1_13·b_1_22·b_3_10
       + b_1_13·b_1_25 + b_1_14·b_1_2·b_3_10 + b_1_14·b_1_2·b_3_8 + b_1_14·b_1_24
       + b_1_15·b_1_23 + b_4_16·b_1_2·b_3_9 + b_4_16·b_1_12·b_1_22
       + b_4_16·b_1_13·b_1_2 + b_2_4·b_6_32 + b_2_4·b_2_5·b_4_16 + b_2_42·b_1_2·b_3_10
       + b_2_42·b_4_16 + b_2_43·b_2_5 + b_2_42·b_2_5·a_1_0·b_1_2
  34. a_1_0·b_7_42 + b_2_42·a_1_0·b_3_9 + b_2_42·b_2_5·a_1_0·b_1_2
  35. b_3_8·b_5_21 + b_1_22·b_3_8·b_3_10 + b_1_1·b_7_42 + b_1_1·b_1_2·b_3_8·b_3_10
       + b_1_12·b_3_8·b_3_10 + b_1_12·b_1_23·b_3_10 + b_1_12·b_1_26 + b_1_13·b_5_21
       + b_1_13·b_1_25 + b_1_14·b_1_2·b_3_10 + b_1_14·b_1_24 + b_1_15·b_3_10
       + b_1_15·b_1_23 + b_1_16·b_1_22 + b_4_16·b_1_24 + b_4_16·b_1_13·b_1_2
       + b_2_42·a_1_0·b_3_10
  36. b_6_32·b_3_9 + b_6_32·b_3_8 + b_4_16·b_5_23 + b_4_16·b_5_21 + b_4_16·b_1_22·b_3_8
       + b_4_16·b_1_25 + b_4_16·b_1_1·b_1_2·b_3_10 + b_4_16·b_1_1·b_1_2·b_3_8
       + b_4_16·b_1_12·b_3_10 + b_4_162·b_1_2 + b_2_4·b_6_32·b_1_2 + b_2_4·b_4_16·b_3_10
       + b_2_4·b_4_16·b_3_9 + b_2_4·b_2_5·b_4_16·b_1_2 + b_2_42·b_4_16·b_1_2 + b_2_43·b_3_10
       + b_2_42·a_1_0·b_1_2·b_3_10 + b_2_42·b_4_16·a_1_0
  37. b_2_5·b_7_42 + b_2_43·b_3_10 + b_2_42·a_1_0·b_1_2·b_3_10 + b_2_43·b_2_5·a_1_0
  38. b_2_4·b_7_42 + b_2_4·b_4_16·b_3_10 + b_2_4·b_4_16·b_3_9 + b_2_4·b_2_5·b_4_16·b_1_2
       + b_2_42·b_5_23 + b_2_42·b_4_16·b_1_2 + b_2_43·b_3_10 + b_2_43·b_3_9
       + b_2_42·a_1_0·b_1_2·b_3_10
  39. b_1_22·b_7_42 + b_1_26·b_3_10 + b_1_26·b_3_8 + b_1_1·b_1_2·b_7_42
       + b_1_1·b_1_25·b_3_8 + b_1_1·b_1_28 + b_1_12·b_7_42 + b_1_12·b_1_24·b_3_10
       + b_1_12·b_1_27 + b_1_13·b_1_23·b_3_8 + b_1_13·b_1_26 + b_1_14·b_5_21
       + b_1_15·b_1_2·b_3_10 + b_1_15·b_1_2·b_3_8 + b_1_16·b_3_8 + b_1_16·b_1_23
       + b_1_17·b_1_22 + b_6_32·b_3_8 + b_6_32·b_1_13 + b_4_16·b_1_22·b_3_8
       + b_4_16·b_1_12·b_3_8 + b_4_16·b_1_12·b_1_23 + b_4_16·b_1_13·b_1_22
       + b_4_162·b_1_1 + b_2_42·a_1_0·b_1_2·b_3_10
  40. b_5_232 + b_5_212 + b_1_1·b_1_26·b_3_8 + b_1_1·b_1_29 + b_1_12·b_1_25·b_3_8
       + b_1_13·b_1_24·b_3_10 + b_1_13·b_1_24·b_3_8 + b_1_14·b_3_8·b_3_10
       + b_1_14·b_1_2·b_5_21 + b_1_14·b_1_23·b_3_10 + b_1_15·b_1_22·b_3_8
       + b_1_17·b_3_10 + b_1_17·b_3_8 + b_6_32·b_1_14 + b_4_16·b_1_13·b_3_8
       + b_4_16·b_1_13·b_1_23 + b_4_16·b_1_14·b_1_22 + b_4_162·b_1_22
       + b_2_4·b_4_162 + b_2_42·b_2_5·b_4_16 + b_2_43·b_1_2·b_3_10
  41. b_5_232 + b_5_21·b_5_23 + b_1_24·b_3_8·b_3_10 + b_1_27·b_3_10
       + b_1_1·b_1_2·b_3_10·b_5_21 + b_1_1·b_1_23·b_3_8·b_3_10 + b_1_12·b_3_10·b_5_21
       + b_1_12·b_1_22·b_3_8·b_3_10 + b_1_12·b_1_25·b_3_10 + b_1_13·b_7_42
       + b_1_13·b_1_2·b_3_8·b_3_10 + b_1_14·b_3_8·b_3_10 + b_1_14·b_1_26 + b_1_15·b_5_21
       + b_1_15·b_1_22·b_3_10 + b_1_15·b_1_22·b_3_8 + b_1_16·b_1_2·b_3_8 + b_1_17·b_3_10
       + b_1_18·b_1_22 + b_6_32·b_1_1·b_3_8 + b_6_32·b_1_1·b_1_23
       + b_6_32·b_1_12·b_1_22 + b_4_16·b_1_2·b_5_21 + b_4_16·b_1_23·b_3_8
       + b_4_16·b_1_26 + b_4_16·b_1_1·b_1_25 + b_4_16·b_1_12·b_1_24
       + b_4_16·b_1_13·b_1_23 + b_4_162·b_1_22 + b_4_162·b_1_12 + b_2_5·b_4_162
       + b_2_4·b_4_162 + b_2_4·b_2_5·b_6_32 + b_2_43·b_1_2·b_3_10 + b_2_44·b_2_5
       + b_2_43·a_1_0·b_3_10 + b_2_43·a_1_0·b_3_9
  42. b_5_232 + b_5_21·b_5_23 + b_3_8·b_7_42 + b_1_27·b_3_10 + b_1_210
       + b_1_1·b_1_2·b_3_10·b_5_21 + b_1_1·b_1_29 + b_1_12·b_1_25·b_3_10
       + b_1_12·b_1_25·b_3_8 + b_1_13·b_1_2·b_3_8·b_3_10 + b_1_13·b_1_24·b_3_10
       + b_1_14·b_1_2·b_5_21 + b_1_14·b_1_26 + b_1_15·b_1_22·b_3_8 + b_1_15·b_1_25
       + b_1_16·b_1_2·b_3_8 + b_1_16·b_1_24 + b_6_32·b_1_24 + b_6_32·b_1_1·b_1_23
       + b_6_32·b_1_12·b_1_22 + b_4_16·b_1_2·b_5_21 + b_4_16·b_1_23·b_3_8
       + b_4_16·b_1_1·b_5_21 + b_4_16·b_1_1·b_1_22·b_3_10 + b_4_16·b_1_1·b_1_22·b_3_8
       + b_4_16·b_1_1·b_1_25 + b_4_16·b_1_12·b_1_2·b_3_10 + b_4_16·b_1_12·b_1_2·b_3_8
       + b_4_16·b_1_12·b_1_24 + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_13·b_1_23
       + b_4_16·b_1_14·b_1_22 + b_4_16·b_1_15·b_1_2 + b_4_162·b_1_22 + b_2_5·b_4_162
       + b_2_4·b_4_162 + b_2_4·b_2_5·b_6_32 + b_2_43·b_1_2·b_3_10 + b_2_44·b_2_5
       + b_2_43·a_1_0·b_3_10 + b_2_43·a_1_0·b_3_9
  43. b_5_232 + b_5_21·b_5_23 + b_3_9·b_7_42 + b_1_27·b_3_10 + b_1_210
       + b_1_1·b_1_2·b_3_10·b_5_21 + b_1_1·b_1_29 + b_1_12·b_1_25·b_3_10
       + b_1_12·b_1_25·b_3_8 + b_1_13·b_1_2·b_3_8·b_3_10 + b_1_13·b_1_24·b_3_10
       + b_1_14·b_1_2·b_5_21 + b_1_14·b_1_26 + b_1_15·b_1_22·b_3_8 + b_1_15·b_1_25
       + b_1_16·b_1_2·b_3_8 + b_1_16·b_1_24 + b_6_32·b_1_24 + b_6_32·b_1_1·b_1_23
       + b_6_32·b_1_12·b_1_22 + b_4_16·b_1_2·b_5_21 + b_4_16·b_1_23·b_3_8
       + b_4_16·b_1_1·b_5_21 + b_4_16·b_1_1·b_1_22·b_3_10 + b_4_16·b_1_1·b_1_22·b_3_8
       + b_4_16·b_1_1·b_1_25 + b_4_16·b_1_12·b_1_2·b_3_10 + b_4_16·b_1_12·b_1_2·b_3_8
       + b_4_16·b_1_12·b_1_24 + b_4_16·b_1_13·b_3_10 + b_4_16·b_1_13·b_1_23
       + b_4_16·b_1_14·b_1_22 + b_4_16·b_1_15·b_1_2 + b_4_162·b_1_22
       + b_2_4·b_4_16·b_1_2·b_3_10 + b_2_4·b_4_16·b_1_2·b_3_9 + b_2_42·b_6_32
       + b_2_42·b_2_5·b_4_16 + b_2_43·b_1_2·b_3_9 + b_2_44·b_2_5 + b_2_43·a_1_0·b_3_10
       + b_2_43·a_1_0·b_3_9
  44. b_5_212 + b_1_1·b_1_26·b_3_8 + b_1_1·b_1_29 + b_1_12·b_1_22·b_3_8·b_3_10
       + b_1_12·b_1_25·b_3_10 + b_1_12·b_1_25·b_3_8 + b_1_14·b_3_8·b_3_10
       + b_1_14·b_1_2·b_5_21 + b_1_14·b_1_23·b_3_8 + b_1_15·b_5_21 + b_1_15·b_1_22·b_3_8
       + b_1_16·b_1_2·b_3_10 + b_1_16·b_1_2·b_3_8 + b_1_17·b_1_23 + b_1_19·b_1_2
       + b_4_16·b_1_26 + b_4_16·b_1_1·b_5_21 + b_4_16·b_1_1·b_1_22·b_3_10
       + b_4_16·b_1_1·b_1_22·b_3_8 + b_4_16·b_1_1·b_1_25 + b_4_16·b_1_12·b_1_2·b_3_8
       + b_4_16·b_1_12·b_1_24 + b_4_16·b_1_13·b_1_23 + b_4_16·b_1_16
       + b_4_162·b_1_22 + b_4_162·b_1_1·b_1_2 + b_2_5·b_4_162 + c_8_57·b_1_12
  45. b_6_32·b_5_23 + b_6_32·b_5_21 + b_6_32·b_1_22·b_3_8 + b_6_32·b_1_25
       + b_6_32·b_1_1·b_1_2·b_3_10 + b_6_32·b_1_1·b_1_2·b_3_8 + b_6_32·b_1_12·b_3_10
       + b_4_16·b_6_32·b_1_2 + b_4_162·b_3_9 + b_4_162·b_3_8 + b_2_4·b_4_16·b_5_23
       + b_2_4·b_4_162·b_1_2 + b_2_4·b_2_5·b_6_32·b_1_2 + b_2_42·b_2_5·b_4_16·b_1_2
       + b_2_43·b_5_21 + b_2_44·b_3_10 + b_2_44·b_2_5·a_1_0
  46. b_1_1·b_3_10·b_7_42 + b_1_1·b_1_24·b_3_8·b_3_10 + b_1_1·b_1_27·b_3_10
       + b_1_1·b_1_210 + b_1_12·b_1_23·b_3_8·b_3_10 + b_1_13·b_1_2·b_7_42
       + b_1_13·b_1_25·b_3_10 + b_1_13·b_1_28 + b_1_14·b_7_42
       + b_1_14·b_1_2·b_3_8·b_3_10 + b_1_14·b_1_24·b_3_10 + b_1_15·b_3_8·b_3_10
       + b_1_15·b_1_2·b_5_21 + b_1_15·b_1_23·b_3_10 + b_1_15·b_1_23·b_3_8
       + b_1_15·b_1_26 + b_1_16·b_1_22·b_3_8 + b_1_16·b_1_25 + b_1_17·b_1_2·b_3_10
       + b_1_17·b_1_2·b_3_8 + b_1_18·b_3_10 + b_1_18·b_1_23 + b_1_19·b_1_22
       + b_1_110·b_1_2 + b_6_32·b_5_21 + b_6_32·b_1_22·b_3_10 + b_6_32·b_1_1·b_1_2·b_3_10
       + b_6_32·b_1_14·b_1_2 + b_6_32·b_1_15 + b_4_16·b_7_42 + b_4_16·b_1_24·b_3_10
       + b_4_16·b_1_24·b_3_8 + b_4_16·b_1_1·b_1_2·b_5_21 + b_4_16·b_1_1·b_1_23·b_3_10
       + b_4_16·b_1_1·b_1_26 + b_4_16·b_1_12·b_1_22·b_3_10
       + b_4_16·b_1_12·b_1_22·b_3_8 + b_4_16·b_1_12·b_1_25 + b_4_16·b_6_32·b_1_1
       + b_4_162·b_3_9 + b_4_162·b_1_12·b_1_2 + b_4_162·b_1_13 + b_2_4·b_4_16·b_5_23
       + b_2_4·b_4_16·b_5_21 + b_2_4·b_4_162·b_1_2 + b_2_42·b_4_16·b_3_10
       + b_2_42·b_4_16·b_3_9 + b_2_43·b_5_21 + c_8_57·b_1_1·b_1_22 + c_8_57·b_1_12·b_1_2
       + c_8_57·b_1_13
  47. b_5_23·b_7_42 + b_5_21·b_7_42 + b_1_26·b_3_8·b_3_10 + b_1_29·b_3_8
       + b_1_1·b_1_28·b_3_8 + b_1_12·b_1_24·b_3_8·b_3_10 + b_1_13·b_1_26·b_3_10
       + b_1_13·b_1_29 + b_1_14·b_1_25·b_3_10 + b_1_14·b_1_28 + b_1_15·b_7_42
       + b_1_15·b_1_2·b_3_8·b_3_10 + b_1_15·b_1_24·b_3_10 + b_1_15·b_1_27
       + b_1_16·b_3_8·b_3_10 + b_1_16·b_1_2·b_5_21 + b_1_16·b_1_23·b_3_8 + b_1_17·b_5_21
       + b_1_17·b_1_25 + b_1_18·b_1_2·b_3_10 + b_1_18·b_1_2·b_3_8 + b_1_19·b_3_10
       + b_1_19·b_1_23 + b_6_32·b_1_2·b_5_21 + b_6_32·b_1_23·b_3_10 + b_6_32·b_1_23·b_3_8
       + b_6_32·b_1_1·b_5_21 + b_6_32·b_1_12·b_1_2·b_3_10 + b_6_32·b_1_12·b_1_2·b_3_8
       + b_6_32·b_1_12·b_1_24 + b_6_32·b_1_13·b_3_10 + b_6_32·b_1_13·b_1_23
       + b_6_32·b_1_15·b_1_2 + b_6_32·b_1_16 + b_6_322 + b_4_16·b_1_22·b_3_8·b_3_10
       + b_4_16·b_1_1·b_7_42 + b_4_16·b_1_1·b_1_2·b_3_8·b_3_10 + b_4_16·b_1_1·b_1_24·b_3_10
       + b_4_16·b_1_1·b_1_27 + b_4_16·b_1_12·b_1_23·b_3_10 + b_4_16·b_1_13·b_5_21
       + b_4_16·b_1_13·b_1_25 + b_4_16·b_1_14·b_1_2·b_3_8 + b_4_16·b_1_15·b_3_10
       + b_4_16·b_1_15·b_3_8 + b_4_16·b_1_15·b_1_23 + b_4_16·b_1_18
       + b_4_16·b_6_32·b_1_22 + b_4_162·b_1_2·b_3_8 + b_4_162·b_1_1·b_3_10
       + b_4_162·b_1_1·b_3_8 + b_4_162·b_1_1·b_1_23 + b_4_162·b_1_12·b_1_22
       + b_4_162·b_1_13·b_1_2 + b_4_163 + b_2_5·b_4_16·b_6_32 + b_2_4·b_4_16·b_1_2·b_5_23
       + b_2_4·b_4_16·b_1_2·b_5_21 + b_2_4·b_4_16·b_6_32 + b_2_42·b_4_16·b_1_2·b_3_10
       + b_2_42·b_4_16·b_1_2·b_3_9 + b_2_42·b_4_162 + b_2_43·b_6_32
       + b_2_43·b_2_5·b_4_16 + b_2_44·b_4_16 + b_2_44·a_1_0·b_3_9
       + b_2_44·b_2_5·a_1_0·b_1_2 + c_8_57·b_1_24 + c_8_57·b_1_1·b_1_23
       + c_8_57·b_1_12·b_1_22
  48. b_5_23·b_7_42 + b_5_21·b_7_42 + b_1_26·b_3_8·b_3_10 + b_1_29·b_3_10 + b_1_29·b_3_8
       + b_1_212 + b_1_1·b_1_25·b_3_8·b_3_10 + b_1_13·b_1_26·b_3_10
       + b_1_14·b_3_10·b_5_21 + b_1_14·b_1_22·b_3_8·b_3_10 + b_1_15·b_7_42
       + b_1_15·b_1_2·b_3_8·b_3_10 + b_1_15·b_1_24·b_3_10 + b_1_15·b_1_24·b_3_8
       + b_1_15·b_1_27 + b_1_16·b_1_23·b_3_8 + b_1_17·b_5_21 + b_1_17·b_1_22·b_3_10
       + b_1_17·b_1_22·b_3_8 + b_1_17·b_1_25 + b_1_18·b_1_24 + b_1_19·b_3_10
       + b_1_19·b_3_8 + b_1_110·b_1_22 + b_1_111·b_1_2 + b_6_32·b_1_2·b_5_21
       + b_6_32·b_1_23·b_3_10 + b_6_32·b_1_23·b_3_8 + b_6_32·b_1_26 + b_6_32·b_1_1·b_5_21
       + b_6_32·b_1_1·b_1_25 + b_6_32·b_1_12·b_1_2·b_3_10 + b_6_32·b_1_12·b_1_2·b_3_8
       + b_6_32·b_1_13·b_3_10 + b_6_32·b_1_13·b_3_8 + b_6_32·b_1_13·b_1_23
       + b_6_32·b_1_14·b_1_22 + b_6_32·b_1_15·b_1_2 + b_4_16·b_1_25·b_3_10
       + b_4_16·b_1_28 + b_4_16·b_1_1·b_7_42 + b_4_16·b_1_1·b_1_24·b_3_10
       + b_4_16·b_1_1·b_1_24·b_3_8 + b_4_16·b_1_12·b_3_8·b_3_10
       + b_4_16·b_1_13·b_1_22·b_3_10 + b_4_16·b_1_15·b_3_10 + b_4_16·b_1_15·b_1_23
       + b_4_16·b_1_16·b_1_22 + b_4_16·b_1_17·b_1_2 + b_4_16·b_6_32·b_1_1·b_1_2
       + b_4_16·b_6_32·b_1_12 + b_4_162·b_1_2·b_3_9 + b_4_162·b_1_1·b_3_8
       + b_4_162·b_1_1·b_1_23 + b_4_162·b_1_12·b_1_22 + b_4_162·b_1_13·b_1_2
       + b_2_5·b_4_16·b_6_32 + b_2_4·b_4_16·b_1_2·b_5_23 + b_2_4·b_4_16·b_1_2·b_5_21
       + b_2_4·b_4_16·b_6_32 + b_2_42·b_4_16·b_1_2·b_3_10 + b_2_42·b_4_16·b_1_2·b_3_9
       + b_2_43·b_6_32 + b_2_43·b_2_5·b_4_16 + b_2_44·b_4_16 + b_2_45·b_2_5
       + b_2_44·b_2_5·a_1_0·b_1_2 + c_8_57·b_1_1·b_1_23 + c_8_57·b_1_14
  49. b_5_23·b_7_42 + b_1_29·b_3_10 + b_1_29·b_3_8 + b_1_212 + b_1_1·b_1_25·b_3_8·b_3_10
       + b_1_1·b_1_28·b_3_10 + b_1_1·b_1_28·b_3_8 + b_1_1·b_1_211 + b_1_12·b_1_27·b_3_10
       + b_1_12·b_1_210 + b_1_13·b_1_2·b_3_10·b_5_21 + b_1_13·b_1_26·b_3_10
       + b_1_14·b_1_22·b_3_8·b_3_10 + b_1_14·b_1_25·b_3_10 + b_1_15·b_1_24·b_3_8
       + b_1_15·b_1_27 + b_1_16·b_1_26 + b_1_17·b_1_22·b_3_8 + b_1_17·b_1_25
       + b_1_18·b_1_2·b_3_10 + b_1_18·b_1_2·b_3_8 + b_1_18·b_1_24 + b_1_19·b_3_10
       + b_1_19·b_3_8 + b_1_110·b_1_22 + b_6_32·b_3_8·b_3_10 + b_6_32·b_1_2·b_5_21
       + b_6_32·b_1_23·b_3_10 + b_6_32·b_1_23·b_3_8 + b_6_32·b_1_26 + b_6_32·b_1_1·b_5_21
       + b_6_32·b_1_1·b_1_22·b_3_8 + b_6_32·b_1_1·b_1_25 + b_6_32·b_1_14·b_1_22
       + b_6_32·b_1_15·b_1_2 + b_4_16·b_1_25·b_3_10 + b_4_16·b_1_28
       + b_4_16·b_1_1·b_1_2·b_3_8·b_3_10 + b_4_16·b_1_1·b_1_27
       + b_4_16·b_1_12·b_3_8·b_3_10 + b_4_16·b_1_12·b_1_26
       + b_4_16·b_1_13·b_1_22·b_3_10 + b_4_16·b_1_13·b_1_25
       + b_4_16·b_1_14·b_1_2·b_3_10 + b_4_16·b_1_15·b_3_10 + b_4_16·b_1_16·b_1_22
       + b_4_16·b_1_18 + b_4_16·b_6_32·b_1_22 + b_4_16·b_6_32·b_1_12
       + b_4_162·b_1_2·b_3_9 + b_4_162·b_1_24 + b_4_162·b_1_1·b_3_10
       + b_4_162·b_1_1·b_3_8 + b_4_162·b_1_14 + b_2_5·b_4_16·b_6_32
       + b_2_4·b_4_16·b_1_2·b_5_23 + b_2_4·b_4_16·b_1_2·b_5_21 + b_2_4·b_4_16·b_6_32
       + b_2_42·b_4_16·b_1_2·b_3_10 + b_2_42·b_4_16·b_1_2·b_3_9 + b_2_42·b_2_5·b_6_32
       + b_2_43·b_1_2·b_5_21 + b_2_43·b_6_32 + b_2_44·b_4_16 + b_2_44·a_1_0·b_3_10
       + b_2_44·a_1_0·b_3_9 + b_2_44·b_2_5·a_1_0·b_1_2 + c_8_57·b_1_1·b_3_8
       + c_8_57·b_1_1·b_1_23
  50. b_1_27·b_3_8·b_3_10 + b_1_210·b_3_8 + b_1_1·b_1_26·b_3_8·b_3_10
       + b_1_1·b_1_29·b_3_8 + b_1_12·b_1_28·b_3_10 + b_1_13·b_1_24·b_3_8·b_3_10
       + b_1_13·b_1_27·b_3_10 + b_1_13·b_1_210 + b_1_14·b_1_23·b_3_8·b_3_10
       + b_1_14·b_1_26·b_3_10 + b_1_15·b_1_2·b_7_42 + b_1_15·b_1_25·b_3_10
       + b_1_15·b_1_25·b_3_8 + b_1_16·b_1_24·b_3_10 + b_1_16·b_1_24·b_3_8
       + b_1_17·b_3_8·b_3_10 + b_1_17·b_1_23·b_3_10 + b_1_17·b_1_23·b_3_8
       + b_1_18·b_5_21 + b_1_18·b_1_22·b_3_8 + b_1_18·b_1_25 + b_1_19·b_1_2·b_3_10
       + b_1_19·b_1_2·b_3_8 + b_1_19·b_1_24 + b_1_110·b_3_10 + b_1_110·b_3_8
       + b_1_110·b_1_23 + b_1_111·b_1_22 + b_1_112·b_1_2 + b_6_32·b_7_42
       + b_6_32·b_1_24·b_3_10 + b_6_32·b_1_1·b_1_23·b_3_10 + b_6_32·b_1_12·b_1_22·b_3_10
       + b_6_32·b_1_12·b_1_22·b_3_8 + b_6_32·b_1_12·b_1_25 + b_6_32·b_1_13·b_1_24
       + b_6_32·b_1_15·b_1_22 + b_6_32·b_1_17 + b_6_322·b_1_1
       + b_4_16·b_1_23·b_3_8·b_3_10 + b_4_16·b_1_26·b_3_10 + b_4_16·b_1_26·b_3_8
       + b_4_16·b_1_1·b_1_2·b_7_42 + b_4_16·b_1_1·b_1_22·b_3_8·b_3_10
       + b_4_16·b_1_1·b_1_25·b_3_10 + b_4_16·b_1_1·b_1_25·b_3_8
       + b_4_16·b_1_12·b_1_2·b_3_8·b_3_10 + b_4_16·b_1_12·b_1_24·b_3_8
       + b_4_16·b_1_13·b_3_8·b_3_10 + b_4_16·b_1_13·b_1_23·b_3_8
       + b_4_16·b_1_14·b_1_22·b_3_10 + b_4_16·b_1_14·b_1_22·b_3_8
       + b_4_16·b_1_14·b_1_25 + b_4_16·b_1_15·b_1_2·b_3_10 + b_4_16·b_1_15·b_1_24
       + b_4_16·b_1_16·b_3_8 + b_4_16·b_1_19 + b_4_16·b_6_32·b_1_1·b_1_22
       + b_4_162·b_5_23 + b_4_162·b_1_22·b_3_10 + b_4_162·b_1_22·b_3_8
       + b_4_162·b_1_25 + b_4_162·b_1_1·b_1_24 + b_4_162·b_1_12·b_3_10
       + b_4_162·b_1_12·b_3_8 + b_4_162·b_1_13·b_1_22 + b_4_163·b_1_2 + b_4_163·b_1_1
       + b_2_5·b_4_16·b_6_32·b_1_2 + b_2_4·b_4_16·b_6_32·b_1_2 + b_2_4·b_4_162·b_3_10
       + b_2_42·b_4_16·b_5_21 + b_2_42·b_4_162·b_1_2 + b_2_42·b_2_5·b_6_32·b_1_2
       + b_2_43·b_6_32·b_1_2 + b_2_43·b_4_16·b_3_9 + b_2_44·b_4_16·b_1_2 + b_2_45·b_3_10
       + b_2_44·b_4_16·a_1_0 + c_8_57·b_1_22·b_3_8 + c_8_57·b_1_1·b_1_2·b_3_8
       + c_8_57·b_1_1·b_1_24 + c_8_57·b_1_12·b_3_8 + c_8_57·b_1_14·b_1_2 + c_8_57·b_1_15
  51. b_7_422 + b_1_214 + b_1_12·b_1_26·b_3_8·b_3_10 + b_1_13·b_1_25·b_3_8·b_3_10
       + b_1_13·b_1_28·b_3_10 + b_1_13·b_1_28·b_3_8 + b_1_14·b_1_24·b_3_8·b_3_10
       + b_1_14·b_1_27·b_3_10 + b_1_14·b_1_210 + b_1_15·b_1_2·b_3_10·b_5_21
       + b_1_15·b_1_23·b_3_8·b_3_10 + b_1_15·b_1_26·b_3_10 + b_1_15·b_1_26·b_3_8
       + b_1_15·b_1_29 + b_1_16·b_3_10·b_5_21 + b_1_16·b_1_25·b_3_8 + b_1_17·b_7_42
       + b_1_17·b_1_2·b_3_8·b_3_10 + b_1_17·b_1_24·b_3_10 + b_1_17·b_1_24·b_3_8
       + b_1_18·b_1_2·b_5_21 + b_1_18·b_1_23·b_3_8 + b_1_19·b_5_21 + b_1_110·b_1_2·b_3_8
       + b_1_111·b_1_23 + b_1_113·b_1_2 + b_6_32·b_1_1·b_7_42
       + b_6_32·b_1_1·b_1_24·b_3_10 + b_6_32·b_1_1·b_1_24·b_3_8
       + b_6_32·b_1_12·b_1_23·b_3_10 + b_6_32·b_1_13·b_1_22·b_3_8
       + b_6_32·b_1_14·b_1_2·b_3_10 + b_6_32·b_1_14·b_1_24 + b_6_32·b_1_15·b_3_8
       + b_6_322·b_1_22 + b_6_322·b_1_1·b_1_2 + b_4_16·b_1_210
       + b_4_16·b_1_1·b_1_26·b_3_8 + b_4_16·b_1_1·b_1_29 + b_4_16·b_1_12·b_3_10·b_5_21
       + b_4_16·b_1_12·b_1_2·b_7_42 + b_4_16·b_1_13·b_1_24·b_3_8
       + b_4_16·b_1_14·b_3_8·b_3_10 + b_4_16·b_1_14·b_1_2·b_5_21
       + b_4_16·b_1_14·b_1_23·b_3_10 + b_4_16·b_1_14·b_1_23·b_3_8
       + b_4_16·b_1_15·b_5_21 + b_4_16·b_1_15·b_1_25 + b_4_16·b_1_17·b_3_10
       + b_4_16·b_1_17·b_3_8 + b_4_16·b_1_18·b_1_22 + b_4_16·b_1_19·b_1_2
       + b_4_16·b_1_110 + b_4_16·b_6_32·b_1_1·b_3_8 + b_4_16·b_6_32·b_1_12·b_1_22
       + b_4_16·b_6_32·b_1_13·b_1_2 + b_4_16·b_6_32·b_1_14 + b_4_162·b_1_26
       + b_4_162·b_1_1·b_1_22·b_3_8 + b_4_162·b_1_1·b_1_25
       + b_4_162·b_1_12·b_1_2·b_3_10 + b_4_162·b_1_13·b_3_10 + b_4_162·b_1_13·b_3_8
       + b_4_162·b_1_13·b_1_23 + b_4_162·b_1_14·b_1_22 + b_4_162·b_1_15·b_1_2
       + b_4_162·b_1_16 + b_4_163·b_1_12 + b_2_5·b_4_163 + b_2_4·b_4_162·b_1_2·b_3_10
       + b_2_4·b_4_162·b_1_2·b_3_9 + b_2_4·b_4_163 + b_2_42·b_2_5·b_4_162
       + b_2_43·b_4_162 + b_2_45·b_1_2·b_3_9 + b_2_45·b_4_16 + b_2_45·a_1_0·b_3_10
       + b_2_45·a_1_0·b_3_9 + c_8_57·b_1_13·b_3_10 + c_8_57·b_1_13·b_1_23
       + c_8_57·b_1_14·b_1_22 + c_8_57·b_1_16 + b_4_16·c_8_57·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 17.
  • However, the last relation was already found in degree 14 and the last generator in degree 8.
  • The following is a filter regular homogeneous system of parameters:
    1. c_8_57, a Duflot regular element of degree 8
    2. b_1_24 + b_1_1·b_3_10 + b_1_1·b_3_8 + b_1_1·b_1_23 + b_1_14 + b_4_16 + b_2_42, an element of degree 4
    3. b_1_2·b_5_23 + b_1_2·b_5_21 + b_1_23·b_3_8 + b_1_26 + b_1_1·b_1_25
         + b_1_12·b_1_2·b_3_8 + b_1_12·b_1_24 + b_1_13·b_3_10 + b_1_13·b_3_8
         + b_4_16·b_1_1·b_1_2 + b_4_16·b_1_12 + b_2_4·b_4_16, an element of degree 6
    4. b_1_22, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 7, 14, 16].
  • 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 1

  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. b_3_8 → 0, an element of degree 3
  7. b_3_9 → 0, an element of degree 3
  8. b_3_10 → 0, an element of degree 3
  9. b_4_16 → 0, an element of degree 4
  10. b_5_21 → 0, an element of degree 5
  11. b_5_23 → 0, an element of degree 5
  12. b_6_32 → 0, an element of degree 6
  13. b_7_42 → 0, an element of degree 7
  14. c_8_57 → c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. 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_2_4 → c_1_12, an element of degree 2
  5. b_2_5 → 0, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_3_10 → 0, an element of degree 3
  9. b_4_16 → c_1_24 + c_1_12·c_1_22, an element of degree 4
  10. b_5_21 → 0, an element of degree 5
  11. b_5_23 → c_1_1·c_1_24 + c_1_13·c_1_22, an element of degree 5
  12. b_6_32 → c_1_26 + c_1_1·c_1_25 + c_1_13·c_1_23 + c_1_14·c_1_22, an element of degree 6
  13. b_7_42 → c_1_1·c_1_26 + c_1_12·c_1_25 + c_1_14·c_1_23 + c_1_16·c_1_2, an element of degree 7
  14. c_8_57 → c_1_12·c_1_26 + c_1_13·c_1_25 + c_1_15·c_1_23 + 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

Restriction map to a maximal el. ab. subgp. 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_2_4 → c_1_22, an element of degree 2
  5. b_2_5 → c_1_22, an element of degree 2
  6. b_3_8 → 0, an element of degree 3
  7. b_3_9 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  8. b_3_10 → c_1_1·c_1_22 + c_1_12·c_1_2, an element of degree 3
  9. b_4_16 → c_1_12·c_1_22 + c_1_14, an element of degree 4
  10. b_5_21 → c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  11. b_5_23 → c_1_1·c_1_24 + c_1_12·c_1_23, an element of degree 5
  12. b_6_32 → c_1_26 + c_1_12·c_1_24 + c_1_13·c_1_23 + c_1_15·c_1_2 + c_1_16, an element of degree 6
  13. b_7_42 → c_1_1·c_1_26 + c_1_12·c_1_25, an element of degree 7
  14. c_8_57 → c_1_28 + c_1_13·c_1_25 + c_1_14·c_1_24 + c_1_15·c_1_23 + 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

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_1, 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 → 0, an element of degree 2
  6. b_3_8 → c_1_33 + c_1_1·c_1_22 + c_1_12·c_1_3 + c_1_12·c_1_2, an element of degree 3
  7. b_3_9 → c_1_33 + c_1_1·c_1_22 + c_1_12·c_1_3 + c_1_12·c_1_2, an element of degree 3
  8. b_3_10 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_12 + c_1_02·c_1_1, an element of degree 3
  9. b_4_16 → c_1_22·c_1_32 + c_1_24 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3 + c_1_13·c_1_3
       + c_1_13·c_1_2 + c_1_0·c_1_13 + c_1_02·c_1_12, an element of degree 4
  10. b_5_21 → c_1_2·c_1_34 + c_1_24·c_1_3 + c_1_1·c_1_34 + c_1_1·c_1_22·c_1_32
       + c_1_1·c_1_24 + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_32
       + c_1_13·c_1_2·c_1_3 + c_1_13·c_1_22 + c_1_0·c_1_14 + c_1_04·c_1_1, an element of degree 5
  11. b_5_23 → 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_1·c_1_24 + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_32 + c_1_13·c_1_2·c_1_3
       + c_1_13·c_1_22 + c_1_02·c_1_13 + c_1_04·c_1_1, an element of degree 5
  12. b_6_32 → c_1_24·c_1_32 + c_1_26 + c_1_1·c_1_35 + c_1_1·c_1_2·c_1_34
       + c_1_1·c_1_24·c_1_3 + c_1_1·c_1_25 + c_1_12·c_1_2·c_1_33 + c_1_13·c_1_33
       + c_1_13·c_1_23 + c_1_14·c_1_32 + c_1_15·c_1_3 + c_1_15·c_1_2
       + c_1_0·c_1_1·c_1_34 + c_1_0·c_1_13·c_1_32 + c_1_0·c_1_14·c_1_3 + c_1_0·c_1_15
       + c_1_02·c_1_34 + c_1_04·c_1_32 + c_1_04·c_1_1·c_1_3 + c_1_04·c_1_12, an element of degree 6
  13. b_7_42 → c_1_37 + c_1_2·c_1_36 + c_1_26·c_1_3 + c_1_1·c_1_22·c_1_34
       + c_1_1·c_1_24·c_1_32 + c_1_1·c_1_25·c_1_3 + c_1_1·c_1_26
       + c_1_12·c_1_2·c_1_34 + c_1_12·c_1_22·c_1_33 + c_1_12·c_1_24·c_1_3
       + c_1_12·c_1_25 + c_1_13·c_1_2·c_1_33 + c_1_13·c_1_22·c_1_32
       + c_1_13·c_1_23·c_1_3 + c_1_14·c_1_33 + c_1_14·c_1_2·c_1_32 + c_1_14·c_1_23
       + c_1_15·c_1_32 + c_1_15·c_1_22 + c_1_0·c_1_1·c_1_35
       + c_1_0·c_1_12·c_1_22·c_1_32 + c_1_0·c_1_13·c_1_2·c_1_32
       + c_1_0·c_1_13·c_1_22·c_1_3 + c_1_0·c_1_14·c_1_32 + c_1_0·c_1_14·c_1_2·c_1_3
       + c_1_02·c_1_35 + c_1_02·c_1_1·c_1_22·c_1_32 + c_1_02·c_1_12·c_1_33
       + c_1_02·c_1_12·c_1_2·c_1_32 + c_1_02·c_1_12·c_1_22·c_1_3
       + c_1_02·c_1_13·c_1_32 + c_1_02·c_1_13·c_1_2·c_1_3 + c_1_02·c_1_13·c_1_22
       + c_1_02·c_1_14·c_1_3 + c_1_02·c_1_14·c_1_2 + c_1_02·c_1_15 + c_1_04·c_1_33
       + c_1_04·c_1_1·c_1_22 + c_1_04·c_1_12·c_1_3 + c_1_04·c_1_12·c_1_2
       + c_1_04·c_1_13, an element of degree 7
  14. c_8_57 → c_1_38 + c_1_2·c_1_37 + c_1_26·c_1_32 + c_1_1·c_1_25·c_1_32
       + c_1_12·c_1_2·c_1_35 + c_1_12·c_1_24·c_1_32 + c_1_12·c_1_26
       + c_1_13·c_1_22·c_1_33 + c_1_13·c_1_23·c_1_32 + c_1_13·c_1_25
       + c_1_14·c_1_34 + c_1_14·c_1_24 + c_1_15·c_1_2·c_1_32 + c_1_15·c_1_22·c_1_3
       + c_1_15·c_1_23 + c_1_16·c_1_32 + c_1_16·c_1_2·c_1_3 + c_1_16·c_1_22
       + c_1_17·c_1_2 + c_1_0·c_1_1·c_1_36 + c_1_0·c_1_1·c_1_22·c_1_34
       + c_1_0·c_1_1·c_1_24·c_1_32 + c_1_0·c_1_12·c_1_22·c_1_33
       + c_1_0·c_1_12·c_1_24·c_1_3 + c_1_0·c_1_13·c_1_2·c_1_33 + c_1_0·c_1_14·c_1_33
       + c_1_0·c_1_15·c_1_32 + c_1_0·c_1_15·c_1_2·c_1_3 + c_1_02·c_1_36
       + c_1_02·c_1_22·c_1_34 + c_1_02·c_1_24·c_1_32
       + c_1_02·c_1_1·c_1_22·c_1_33 + c_1_02·c_1_1·c_1_24·c_1_3
       + c_1_02·c_1_12·c_1_2·c_1_33 + c_1_02·c_1_12·c_1_22·c_1_32
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_13·c_1_33 + c_1_02·c_1_15·c_1_3
       + c_1_02·c_1_15·c_1_2 + c_1_02·c_1_16 + c_1_03·c_1_15
       + c_1_04·c_1_22·c_1_32 + c_1_04·c_1_24 + c_1_04·c_1_12·c_1_32
       + c_1_04·c_1_12·c_1_2·c_1_3 + c_1_04·c_1_13·c_1_3 + c_1_04·c_1_13·c_1_2
       + c_1_04·c_1_14 + c_1_05·c_1_13 + c_1_06·c_1_12 + c_1_08, an element of degree 8

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