Cohomology of group number 1933 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 8.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 2.
  • It has 4 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 3.


Structure of the cohomology ring

General information

  • The cohomology ring is of dimension 3 and depth 2.
  • The depth coincides with the Duflot bound.
  • The Poincaré series is
    ( − 1) · (t8  +  t7  +  2·t5  +  t4  +  t3  +  t2  +  t  +  1)

    (t  −  1)3 · (t2  +  1)2 · (t4  +  1)
  • The a-invariants are -∞,-∞,-5,-3. 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_2, a nilpotent element of degree 1
  2. b_1_0, an element of degree 1
  3. b_1_1, an element of degree 1
  4. b_1_3, an element of degree 1
  5. a_3_11, a nilpotent element of degree 3
  6. b_3_10, an element of degree 3
  7. b_4_15, an element of degree 4
  8. c_4_16, a Duflot regular element of degree 4
  9. b_5_22, an element of degree 5
  10. b_5_23, an element of degree 5
  11. b_5_24, an element of degree 5
  12. b_7_40, an element of degree 7
  13. b_8_47, an element of degree 8
  14. c_8_49, 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 57 minimal relations of maximal degree 16:

  1. a_1_2·b_1_0
  2. b_1_0·b_1_3 + b_1_0·b_1_1 + a_1_2·b_1_1
  3. a_1_2·b_1_1·b_1_3
  4. b_1_1·b_1_32 + b_1_12·b_1_3 + b_1_0·b_1_12 + a_1_2·b_1_12 + a_1_23
  5. b_1_0·a_3_11
  6. b_1_3·b_3_10 + b_1_1·b_3_10 + b_1_1·a_3_11
  7. a_1_2·b_3_10
  8. a_1_23·b_1_32
  9. b_1_12·b_3_10 + b_1_14·b_1_3 + b_1_0·b_1_14 + b_4_15·b_1_3 + b_1_32·a_3_11
       + b_1_1·b_1_3·a_3_11 + b_1_12·a_3_11 + a_1_2·b_1_14 + a_1_22·b_1_33
       + a_1_22·a_3_11
  10. b_1_0·b_1_14 + b_4_15·b_1_0 + b_1_12·a_3_11 + a_1_2·b_1_14
  11. b_1_1·b_1_3·a_3_11 + b_1_12·a_3_11 + b_4_15·a_1_2 + a_1_2·b_1_3·a_3_11
  12. a_3_112 + a_1_2·b_1_32·a_3_11 + a_1_22·b_1_34 + a_1_23·a_3_11 + c_4_16·a_1_22
  13. b_4_15·b_1_0·b_1_1 + a_3_11·b_3_10 + b_1_13·a_3_11
  14. b_3_102 + b_1_15·b_1_3 + b_1_03·b_3_10 + b_1_13·a_3_11 + b_4_15·a_1_2·b_1_1
       + c_4_16·b_1_02
  15. b_3_102 + b_1_15·b_1_3 + b_1_03·b_3_10 + b_1_13·a_3_11 + a_1_2·b_5_22
       + a_1_22·b_1_3·a_3_11 + a_1_23·a_3_11 + c_4_16·b_1_02 + c_4_16·a_1_2·b_1_3
       + c_4_16·a_1_2·b_1_1
  16. b_3_102 + b_1_1·b_5_22 + b_1_15·b_1_3 + b_1_0·b_5_23 + b_1_05·b_1_1
       + b_4_15·b_1_1·b_1_3 + b_4_15·b_1_12 + a_3_11·b_3_10 + a_1_23·a_3_11
       + c_4_16·b_1_1·b_1_3 + c_4_16·b_1_12 + c_4_16·a_1_2·b_1_1
  17. b_3_102 + b_1_3·b_5_22 + b_1_1·b_5_22 + b_1_15·b_1_3 + b_1_03·b_3_10
       + b_4_15·b_1_1·b_1_3 + b_4_15·b_1_12 + a_3_11·b_3_10 + a_1_2·b_5_23 + a_3_112
       + a_1_2·b_1_32·a_3_11 + a_1_22·b_1_34 + a_1_22·b_1_3·a_3_11 + c_4_16·b_1_32
       + c_4_16·b_1_12 + c_4_16·b_1_02 + c_4_16·a_1_2·b_1_3 + c_4_16·a_1_2·b_1_1
  18. b_3_102 + b_1_3·b_5_22 + b_1_1·b_5_24 + b_1_1·b_5_23 + b_1_1·b_5_22
       + b_1_02·b_1_1·b_3_10 + b_1_03·b_3_10 + a_1_2·b_1_32·a_3_11 + a_1_23·a_3_11
       + c_4_16·b_1_32 + c_4_16·b_1_1·b_1_3 + c_4_16·b_1_12 + c_4_16·b_1_02
  19. b_1_1·b_5_22 + b_1_0·b_5_24 + b_1_02·b_1_1·b_3_10 + b_4_15·b_1_1·b_1_3
       + b_4_15·b_1_12 + b_1_13·a_3_11 + c_4_16·b_1_1·b_1_3 + c_4_16·b_1_12
       + c_4_16·b_1_0·b_1_1 + c_4_16·b_1_02
  20. b_4_15·b_3_10 + b_4_15·b_1_12·b_1_3 + b_1_1·a_3_11·b_3_10 + b_1_14·a_3_11
       + c_4_16·a_1_2·b_1_12
  21. b_1_1·a_3_11·b_3_10 + b_1_14·a_3_11 + b_4_15·a_3_11 + a_1_2·b_1_33·a_3_11
       + a_1_22·b_1_35 + a_1_22·b_1_32·a_3_11 + c_4_16·a_1_2·b_1_12
       + c_4_16·a_1_22·b_1_3
  22. a_1_2·b_1_3·b_5_23 + a_1_2·b_1_33·a_3_11 + a_1_22·b_1_32·a_3_11
       + a_1_23·b_1_3·a_3_11 + c_4_16·a_1_2·b_1_32 + c_4_16·a_1_22·b_1_3
  23. b_1_32·b_5_23 + b_1_1·b_1_3·b_5_23 + b_1_0·b_1_1·b_5_23 + b_1_03·b_1_1·b_3_10
       + b_1_34·a_3_11 + b_1_14·a_3_11 + a_1_2·b_1_1·b_5_23 + b_4_15·a_1_2·b_1_12
       + a_1_2·b_1_33·a_3_11 + a_1_22·b_5_24 + c_4_16·b_1_33 + c_4_16·b_1_12·b_1_3
       + c_4_16·b_1_02·b_1_1 + c_4_16·a_1_2·b_1_32 + c_4_16·a_1_23
  24. b_4_15·b_1_13·b_1_3 + b_4_15·b_1_14 + b_4_152 + b_4_15·a_1_2·b_1_13
       + a_1_2·b_1_34·a_3_11 + a_1_22·b_1_36 + c_4_16·b_1_13·b_1_3 + c_4_16·b_1_14
       + c_4_16·b_1_0·b_1_13 + c_4_16·a_1_2·b_1_13 + c_4_16·a_1_22·b_1_32
  25. a_3_11·b_5_22 + b_4_15·a_1_2·b_1_13 + a_1_22·b_1_33·a_3_11 + c_4_16·b_1_3·a_3_11
       + c_4_16·b_1_1·a_3_11 + c_4_16·a_1_2·b_1_13 + c_4_16·a_1_23·b_1_3
  26. b_3_10·b_5_24 + b_3_10·b_5_23 + b_1_17·b_1_3 + b_1_05·b_3_10 + b_4_15·b_1_13·b_1_3
       + b_4_15·a_1_2·b_1_13 + c_4_16·b_1_1·b_3_10 + c_4_16·b_1_03·b_1_1 + c_4_16·b_1_04
       + c_4_16·b_1_1·a_3_11 + c_4_16·a_1_2·b_1_13
  27. b_3_10·b_5_23 + b_1_1·b_7_40 + b_1_13·b_5_23 + b_1_17·b_1_3 + b_1_0·b_1_12·b_5_23
       + b_1_04·b_1_1·b_3_10 + b_1_05·b_3_10 + b_4_15·b_1_13·b_1_3 + b_4_15·b_1_14
       + b_1_15·a_3_11 + b_4_15·b_1_1·a_3_11 + b_4_15·a_1_2·b_1_13 + c_4_16·b_1_1·b_3_10
       + c_4_16·b_1_0·b_3_10 + c_4_16·b_1_04 + c_4_16·b_1_1·a_3_11
  28. b_3_10·b_5_23 + b_1_3·b_7_40 + b_1_12·b_1_3·b_5_23 + b_1_17·b_1_3
       + b_1_0·b_1_12·b_5_23 + b_1_04·b_1_1·b_3_10 + b_1_05·b_3_10 + a_3_11·b_5_23
       + a_1_2·b_1_12·b_5_23 + b_4_15·b_1_1·a_3_11 + b_4_15·a_1_2·b_1_13
       + a_1_2·b_1_34·a_3_11 + a_1_22·b_1_33·a_3_11 + c_4_16·b_1_1·b_3_10
       + c_4_16·b_1_0·b_3_10 + c_4_16·b_1_04 + c_4_16·b_1_3·a_3_11 + c_4_16·b_1_1·a_3_11
       + c_4_16·a_1_2·b_1_33 + c_4_16·a_1_2·b_1_13 + c_4_16·a_1_2·a_3_11
       + c_4_16·a_1_22·b_1_32 + c_4_16·a_1_23·b_1_3
  29. b_3_10·b_5_22 + b_1_0·b_7_40 + b_1_0·b_1_12·b_5_23 + b_1_04·b_1_1·b_3_10
       + b_1_07·b_1_1 + b_1_15·a_3_11 + b_4_15·b_1_1·a_3_11 + c_4_16·b_1_0·b_3_10
       + c_4_16·b_1_1·a_3_11
  30. a_1_2·b_7_40 + a_1_2·b_1_12·b_5_23 + b_4_15·a_1_2·b_1_13 + c_4_16·a_1_22·b_1_32
  31. b_1_0·b_1_13·b_5_23 + b_4_15·b_5_22 + b_4_152·b_1_1 + b_1_1·a_3_11·b_5_23
       + a_1_2·b_1_13·b_5_23 + b_4_15·b_1_12·a_3_11 + b_4_152·a_1_2 + b_4_15·c_4_16·b_1_3
       + b_4_15·c_4_16·b_1_1 + b_4_15·c_4_16·a_1_2 + c_4_16·a_1_2·b_1_3·a_3_11
  32. b_1_0·b_1_13·b_5_23 + b_4_15·b_5_24 + b_4_15·b_5_23 + b_4_15·b_5_22 + b_4_15·b_1_15
       + b_4_152·b_1_1 + b_1_3·a_3_11·b_5_24 + b_1_16·a_3_11 + a_1_2·b_1_13·b_5_23
       + b_4_15·b_1_12·a_3_11 + b_4_152·a_1_2 + a_1_2·b_1_35·a_3_11
       + a_1_22·b_1_32·b_5_24 + a_1_22·b_1_37 + c_4_16·b_1_14·b_1_3 + c_4_16·b_1_15
       + b_4_15·c_4_16·b_1_1 + b_4_15·c_4_16·b_1_0 + b_4_15·c_4_16·a_1_2
       + c_4_16·a_1_22·b_1_33
  33. b_1_12·b_7_40 + b_1_18·b_1_3 + b_1_0·b_1_1·b_7_40 + b_1_0·b_1_13·b_5_23
       + b_8_47·b_1_1 + b_4_15·b_5_23 + b_4_152·b_1_1 + b_1_3·a_3_11·b_5_23
       + a_1_2·b_1_13·b_5_23 + b_4_15·b_1_12·a_3_11 + a_1_22·b_1_34·a_3_11
       + c_4_16·b_1_15 + c_4_16·b_1_04·b_1_1 + b_4_15·c_4_16·b_1_3 + b_4_15·c_4_16·b_1_1
       + c_4_16·b_1_32·a_3_11 + c_4_16·b_1_12·a_3_11 + b_4_15·c_4_16·a_1_2
       + c_4_16·a_1_2·b_1_3·a_3_11
  34. b_1_34·b_5_24 + b_1_13·b_1_3·b_5_23 + b_1_18·b_1_3 + b_1_0·b_1_1·b_7_40
       + b_8_47·b_1_3 + b_1_3·a_3_11·b_5_23 + b_1_36·a_3_11 + b_1_16·a_3_11
       + a_1_2·b_1_13·b_5_23 + a_1_2·a_3_11·b_5_24 + a_1_2·b_1_35·a_3_11 + a_1_22·b_1_37
       + c_4_16·b_1_14·b_1_3 + c_4_16·b_1_04·b_1_1 + b_4_15·c_4_16·b_1_3
       + c_4_16·b_1_32·a_3_11 + c_4_16·a_1_2·b_1_34 + c_4_16·a_1_2·b_1_3·a_3_11
  35. b_1_0·b_1_1·b_7_40 + b_1_02·b_7_40 + b_1_04·b_5_23 + b_1_06·b_3_10 + b_1_08·b_1_1
       + b_8_47·b_1_0 + b_4_15·b_5_22 + b_4_152·b_1_1 + b_1_16·a_3_11 + a_1_22·b_1_34·a_3_11
       + b_4_15·c_4_16·b_1_3 + b_4_15·c_4_16·b_1_1 + b_4_15·c_4_16·b_1_0
       + c_4_16·b_1_12·a_3_11
  36. b_1_0·b_1_13·b_5_23 + b_4_15·b_5_22 + b_4_152·b_1_1 + b_1_3·a_3_11·b_5_23
       + a_1_2·b_1_33·b_5_24 + b_8_47·a_1_2 + b_4_15·b_1_12·a_3_11 + b_4_152·a_1_2
       + a_1_22·b_1_37 + a_1_22·b_1_34·a_3_11 + b_4_15·c_4_16·b_1_3 + b_4_15·c_4_16·b_1_1
       + c_4_16·b_1_32·a_3_11 + c_4_16·b_1_12·a_3_11 + b_4_15·c_4_16·a_1_2
       + c_4_16·a_1_2·b_1_3·a_3_11
  37. b_4_15·b_1_0·b_5_23 + a_3_11·b_7_40 + b_1_17·a_3_11 + a_1_22·b_1_35·a_3_11
       + c_4_16·a_3_11·b_3_10 + c_4_16·a_1_2·b_1_15 + c_4_16·a_1_2·b_1_32·a_3_11
       + c_4_16·a_1_23·a_3_11
  38. b_5_232 + b_1_15·b_5_23 + b_1_19·b_1_3 + b_1_07·b_3_10 + b_4_152·b_1_12
       + b_4_152·a_1_2·b_1_1 + a_1_2·b_1_36·a_3_11 + a_1_22·b_1_38 + c_8_49·b_1_12
       + c_4_16·b_1_16 + c_4_16·b_1_06 + b_4_15·c_4_16·b_1_12 + c_4_16·a_3_11·b_3_10
       + c_4_16·b_1_13·a_3_11 + c_4_16·a_1_2·b_1_15 + b_4_15·c_4_16·a_1_2·b_1_1
       + c_4_16·a_1_22·b_1_34 + c_4_162·b_1_32 + c_4_162·b_1_12 + c_4_162·b_1_02
       + c_4_162·a_1_22
  39. b_5_222 + b_1_06·b_1_1·b_3_10 + b_1_09·b_1_1 + b_4_152·b_1_12
       + b_4_15·b_1_13·a_3_11 + b_4_152·a_1_2·b_1_1 + c_8_49·b_1_02
       + c_4_16·b_1_03·b_3_10 + c_4_16·b_1_05·b_1_1 + c_4_16·b_1_06 + c_4_162·b_1_32
       + c_4_162·b_1_12
  40. b_5_23·b_5_24 + b_5_232 + b_5_22·b_5_24 + b_1_15·b_5_23 + b_1_06·b_1_1·b_3_10
       + b_1_07·b_3_10 + b_8_47·b_1_12 + b_4_15·b_1_3·b_5_23 + b_4_15·b_1_1·b_5_23
       + b_4_152·b_1_12 + b_1_32·a_3_11·b_5_24 + b_1_12·a_3_11·b_5_23
       + b_4_15·b_1_13·a_3_11 + b_4_152·a_1_2·b_1_1 + a_1_22·a_3_11·b_5_24
       + a_1_22·b_1_35·a_3_11 + c_8_49·b_1_0·b_1_1 + c_4_16·b_1_1·b_5_23
       + c_4_16·b_1_0·b_5_23 + c_4_16·b_1_0·b_5_22 + c_4_16·b_1_06
       + b_4_15·c_4_16·b_1_1·b_1_3 + c_8_49·a_1_2·b_1_1 + c_4_16·b_1_33·a_3_11
       + c_4_16·a_1_2·b_5_24 + c_4_16·a_1_2·b_5_23 + c_4_16·a_1_23·a_3_11 + c_4_162·b_1_32
       + c_4_162·b_1_1·b_1_3 + c_4_162·b_1_02 + c_4_162·a_1_2·b_1_3
  41. b_5_22·b_5_24 + b_8_47·b_1_0·b_1_1 + b_4_15·b_1_3·b_5_23 + b_4_15·b_1_1·b_5_23
       + b_4_15·b_1_0·b_5_23 + b_4_152·b_1_12 + b_1_17·a_3_11 + a_1_2·b_1_3·a_3_11·b_5_24
       + a_1_2·b_1_36·a_3_11 + a_1_22·b_1_38 + a_1_22·a_3_11·b_5_24 + c_8_49·b_1_0·b_1_1
       + c_4_16·b_1_3·b_5_24 + c_4_16·b_1_1·b_5_23 + c_4_16·b_1_15·b_1_3
       + c_4_16·b_1_0·b_5_23 + c_4_16·b_1_0·b_5_22 + c_4_16·b_1_02·b_1_1·b_3_10
       + c_4_16·b_1_03·b_3_10 + c_4_16·b_1_05·b_1_1 + b_4_15·c_4_16·b_1_1·b_1_3
       + b_4_15·c_4_16·b_1_12 + c_4_16·b_1_33·a_3_11 + c_4_16·b_1_13·a_3_11
       + c_4_16·a_1_2·b_5_23 + c_4_162·b_1_1·b_1_3 + c_4_162·b_1_02 + c_4_162·a_1_2·b_1_3
       + c_4_162·a_1_2·b_1_1 + c_4_162·a_1_22
  42. b_5_22·b_5_23 + b_3_10·b_7_40 + b_1_19·b_1_3 + b_1_05·b_5_23 + b_1_07·b_3_10
       + b_1_09·b_1_1 + b_4_15·b_1_1·b_5_23 + b_4_15·b_1_16 + b_4_15·b_1_0·b_5_23
       + b_4_152·b_1_12 + b_1_12·a_3_11·b_5_23 + b_1_17·a_3_11 + b_8_47·a_1_2·b_1_1
       + b_4_15·b_1_13·a_3_11 + b_4_152·a_1_2·b_1_1 + a_1_22·b_1_35·a_3_11
       + c_8_49·b_1_0·b_1_1 + c_4_16·b_1_3·b_5_23 + c_4_16·b_1_1·b_5_23 + c_4_16·b_1_16
       + c_4_16·b_1_02·b_1_1·b_3_10 + c_4_16·b_1_03·b_3_10 + c_4_16·b_1_06
       + c_4_16·a_3_11·b_3_10 + c_4_16·a_1_2·b_5_23 + c_4_16·a_1_2·b_1_15
       + c_4_162·b_1_02 + c_4_162·a_1_2·b_1_3 + c_4_162·a_1_2·b_1_1 + c_4_162·a_1_22
  43. b_5_242 + b_5_232 + b_1_19·b_1_3 + b_1_07·b_3_10 + b_4_152·b_1_12
       + b_1_37·a_3_11 + b_8_47·a_1_2·b_1_3 + a_1_2·b_1_36·a_3_11 + a_1_22·a_3_11·b_5_24
       + a_1_22·b_1_35·a_3_11 + c_4_16·b_1_36 + c_4_16·b_1_15·b_1_3 + c_4_16·b_1_06
       + c_4_16·a_3_11·b_3_10 + c_8_49·a_1_22 + c_4_16·a_1_2·b_1_32·a_3_11
       + c_4_16·a_1_22·b_1_34 + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·b_1_32
  44. b_5_22·b_5_24 + b_5_22·b_5_23 + b_1_06·b_1_1·b_3_10 + b_1_09·b_1_1 + b_8_47·b_1_02
       + b_4_15·b_1_0·b_5_23 + b_4_152·b_1_12 + b_1_12·a_3_11·b_5_23
       + b_4_15·b_1_13·a_3_11 + b_4_152·a_1_2·b_1_1 + a_1_2·b_1_3·a_3_11·b_5_24
       + a_1_22·b_1_35·a_3_11 + c_4_16·b_1_3·b_5_24 + c_4_16·b_1_3·b_5_23
       + c_4_16·b_1_15·b_1_3 + c_4_16·b_1_0·b_5_23 + c_4_16·b_1_05·b_1_1 + c_4_16·b_1_06
       + b_4_15·c_4_16·b_1_1·b_1_3 + b_4_15·c_4_16·b_1_12 + c_4_16·a_3_11·b_3_10
       + c_4_16·a_1_2·b_1_32·a_3_11 + c_4_16·a_1_22·b_1_3·a_3_11 + c_4_162·b_1_1·b_1_3
       + c_4_162·b_1_02 + c_4_162·a_1_2·b_1_1
  45. b_4_15·b_7_40 + b_4_15·b_1_1·b_1_3·b_5_23 + b_4_15·b_1_12·b_5_23 + b_4_15·b_1_17
       + a_1_22·b_1_36·a_3_11 + c_4_16·b_1_16·b_1_3 + c_4_16·b_1_17
       + b_4_15·c_4_16·b_1_12·b_1_3 + c_4_16·b_1_14·a_3_11 + c_4_16·a_1_2·b_1_1·b_5_23
       + c_4_16·a_1_2·b_1_16 + c_4_16·a_1_2·b_1_33·a_3_11 + c_4_16·a_1_23·b_1_3·a_3_11
  46. b_1_06·b_5_23 + b_1_07·b_1_1·b_3_10 + b_1_08·b_3_10 + b_8_47·b_3_10
       + b_8_47·b_1_02·b_1_1 + b_8_47·b_1_03 + b_4_15·b_1_14·a_3_11
       + b_4_152·a_1_2·b_1_12 + c_4_16·b_1_02·b_5_23 + c_4_16·b_1_02·b_5_22
       + c_4_16·b_1_03·b_1_1·b_3_10 + c_4_16·b_1_06·b_1_1 + b_4_15·c_4_16·b_1_12·b_1_3
       + c_4_16·a_1_2·b_1_1·b_5_23 + b_4_15·c_4_16·a_3_11 + c_4_16·a_1_2·b_1_33·a_3_11
       + c_4_16·a_1_22·b_1_35 + c_4_16·a_1_22·b_1_32·a_3_11 + c_4_162·b_1_02·b_1_1
       + c_4_162·a_1_22·b_1_3
  47. b_1_33·a_3_11·b_5_24 + b_1_13·a_3_11·b_5_23 + b_1_18·a_3_11 + b_8_47·a_3_11
       + b_4_15·a_1_2·b_1_1·b_5_23 + b_4_152·a_1_2·b_1_12 + a_1_2·b_1_37·a_3_11
       + a_1_22·b_1_39 + a_1_22·b_1_3·a_3_11·b_5_24 + c_4_16·b_1_14·a_3_11
       + c_4_16·a_1_2·b_1_1·b_5_23 + c_4_16·a_1_2·b_1_16 + b_4_15·c_4_16·a_3_11
       + b_4_15·c_4_16·a_1_2·b_1_12 + c_4_16·a_1_2·b_1_33·a_3_11
       + c_4_16·a_1_22·b_1_35 + c_4_16·a_1_22·b_1_32·a_3_11
  48. b_5_24·b_7_40 + b_5_23·b_7_40 + b_5_22·b_7_40 + b_1_111·b_1_3 + b_1_08·b_1_1·b_3_10
       + b_1_011·b_1_1 + b_8_47·b_1_04 + b_4_15·b_1_12·b_1_3·b_5_23
       + b_1_14·a_3_11·b_5_23 + b_1_19·a_3_11 + b_4_15·a_3_11·b_5_23
       + b_4_152·a_1_2·b_1_13 + b_8_47·a_1_22·b_1_32 + c_8_49·b_1_0·b_3_10
       + c_8_49·b_1_0·b_1_13 + c_4_16·b_1_1·b_7_40 + c_4_16·b_1_17·b_1_3
       + c_4_16·b_1_0·b_7_40 + c_4_16·b_1_0·b_1_12·b_5_23 + c_4_16·b_1_03·b_5_23
       + c_4_16·b_1_03·b_5_22 + c_4_16·b_1_04·b_1_1·b_3_10 + c_4_16·b_1_05·b_3_10
       + c_4_16·b_1_08 + b_4_15·c_4_16·b_1_14 + b_4_152·c_4_16 + c_8_49·a_1_2·b_1_13
       + c_4_16·b_1_15·a_3_11 + c_4_16·a_1_2·b_1_32·b_5_24 + c_4_16·a_1_2·b_1_12·b_5_23
       + c_4_16·a_1_2·b_1_17 + b_4_15·c_4_16·a_1_2·b_1_13 + c_4_16·a_1_2·b_1_34·a_3_11
       + c_4_16·a_1_22·b_1_33·a_3_11 + c_4_162·b_1_13·b_1_3 + c_4_162·b_1_14
       + c_4_162·b_1_0·b_3_10 + c_4_162·b_1_0·b_1_13 + c_4_162·b_1_03·b_1_1
       + c_4_162·b_1_04 + c_4_162·a_1_2·b_1_13 + c_4_162·a_1_22·b_1_32
       + c_4_162·a_1_23·b_1_3
  49. b_5_24·b_7_40 + b_1_17·b_5_23 + b_1_111·b_1_3 + b_8_47·b_1_03·b_1_1 + b_4_15·b_1_18
       + b_4_153 + b_1_19·a_3_11 + b_4_15·a_3_11·b_5_23 + b_8_47·a_1_22·b_1_32
       + a_1_22·b_1_37·a_3_11 + c_8_49·b_1_1·b_3_10 + c_8_49·b_1_14
       + c_8_49·b_1_0·b_1_13 + c_4_16·b_1_12·b_1_3·b_5_23 + c_4_16·b_1_0·b_7_40
       + c_4_16·b_1_03·b_5_23 + c_4_16·b_1_05·b_3_10 + c_8_49·a_1_2·b_1_13
       + c_4_16·b_1_15·a_3_11 + c_4_16·a_1_2·b_1_32·b_5_24 + c_4_16·a_1_2·b_1_12·b_5_23
       + c_4_16·a_1_2·b_1_17 + b_4_15·c_4_16·a_1_2·b_1_13 + c_4_16·a_1_2·b_1_34·a_3_11
       + c_4_16·a_1_22·b_1_36 + c_4_162·b_1_1·b_3_10 + c_4_162·b_1_13·b_1_3
       + c_4_162·b_1_14 + c_4_162·b_1_0·b_1_13 + c_4_162·b_1_04
       + c_4_162·a_1_22·b_1_32 + c_4_162·a_1_23·b_1_3
  50. b_5_24·b_7_40 + b_5_23·b_7_40 + b_1_111·b_1_3 + b_8_47·b_1_0·b_3_10
       + b_4_15·b_1_13·b_5_23 + b_4_153 + b_1_19·a_3_11 + b_8_47·a_1_2·b_1_13
       + b_4_15·b_1_15·a_3_11 + b_4_152·a_1_2·b_1_13 + b_8_47·a_1_22·b_1_32
       + c_4_16·b_1_1·b_7_40 + c_4_16·b_1_12·b_1_3·b_5_23 + c_4_16·b_1_13·b_5_23
       + c_4_16·b_1_17·b_1_3 + c_4_16·b_1_04·b_1_1·b_3_10 + c_4_16·b_1_05·b_3_10
       + b_4_15·c_4_16·b_1_14 + b_4_152·c_4_16 + c_8_49·a_1_2·b_1_13
       + c_4_16·a_3_11·b_5_23 + c_4_16·b_1_15·a_3_11 + c_4_16·a_1_2·b_1_32·b_5_24
       + c_4_16·a_1_2·b_1_12·b_5_23 + b_4_15·c_4_16·a_1_2·b_1_13
       + c_4_16·a_1_2·b_1_34·a_3_11 + c_4_16·a_1_22·b_1_36
       + c_4_16·a_1_22·b_1_33·a_3_11 + c_4_162·b_1_13·b_1_3 + c_4_162·b_1_14
       + c_4_162·b_1_0·b_1_13 + c_4_162·b_1_3·a_3_11 + c_4_162·a_1_2·b_1_33
       + c_4_162·a_1_2·b_1_13 + c_4_162·a_1_2·a_3_11 + c_4_162·a_1_22·b_1_32
       + c_4_162·a_1_23·b_1_3
  51. b_4_15·b_8_47 + b_8_47·b_1_3·a_3_11 + b_8_47·a_1_22·b_1_32
       + a_1_22·b_1_32·a_3_11·b_5_24 + c_4_16·b_1_12·b_1_3·b_5_23 + c_4_16·b_1_13·b_5_23
       + c_4_16·b_1_0·b_1_12·b_5_23 + b_4_152·c_4_16 + b_4_15·c_4_16·b_1_1·a_3_11
       + b_4_15·c_4_16·a_1_2·b_1_13 + c_4_16·a_1_2·b_1_34·a_3_11
       + c_4_16·a_1_22·b_1_36 + c_4_162·a_1_2·b_1_13 + c_4_162·a_1_22·b_1_32
  52. b_1_09·b_1_1·b_3_10 + b_1_012·b_1_1 + b_8_47·b_5_22 + b_8_47·b_1_02·b_3_10
       + b_8_47·b_1_05 + b_8_47·a_1_2·b_1_14 + b_8_47·a_1_2·b_1_3·a_3_11
       + c_8_49·b_1_0·b_1_1·b_3_10 + c_8_49·b_1_02·b_3_10 + c_8_49·b_1_04·b_1_1
       + c_4_16·b_1_13·b_1_3·b_5_23 + c_4_16·b_1_14·b_5_23 + c_4_16·b_1_05·b_1_1·b_3_10
       + c_4_16·b_1_06·b_3_10 + c_4_16·b_1_09 + c_4_16·b_8_47·b_1_3 + c_4_16·b_8_47·b_1_1
       + c_4_16·b_8_47·b_1_0 + b_4_152·c_4_16·b_1_1 + c_8_49·b_1_12·a_3_11
       + c_8_49·a_1_2·b_1_14 + c_4_16·b_1_1·a_3_11·b_5_23 + c_4_16·a_1_2·b_1_13·b_5_23
       + c_4_16·a_1_2·b_1_18 + b_4_15·c_4_16·b_1_12·a_3_11 + c_4_162·b_1_0·b_1_1·b_3_10
       + c_4_162·b_1_02·b_3_10 + c_4_162·b_1_05 + b_4_15·c_4_162·b_1_0
       + c_4_162·b_1_12·a_3_11 + c_4_162·a_1_2·b_1_14 + b_4_15·c_4_162·a_1_2
       + c_4_162·a_1_2·b_1_3·a_3_11
  53. b_1_09·b_1_1·b_3_10 + b_1_012·b_1_1 + b_8_47·b_5_23 + b_8_47·b_5_22 + b_8_47·b_1_15
       + b_8_47·b_1_04·b_1_1 + b_8_47·b_1_05 + b_8_47·b_1_32·a_3_11
       + b_8_47·a_1_2·b_1_14 + b_4_15·b_1_1·a_3_11·b_5_23 + b_4_15·b_1_16·a_3_11
       + b_4_15·a_1_2·b_1_13·b_5_23 + b_4_153·a_1_2 + a_1_22·b_1_38·a_3_11
       + b_8_47·a_1_22·a_3_11 + c_8_49·b_1_14·b_1_3 + c_8_49·b_1_15
       + c_8_49·b_1_02·b_3_10 + c_8_49·b_1_04·b_1_1 + c_4_16·b_1_13·b_1_3·b_5_23
       + c_4_16·b_1_14·b_5_23 + c_4_16·b_1_18·b_1_3 + c_4_16·b_1_19
       + c_4_16·b_1_04·b_5_23 + c_4_16·b_1_05·b_1_1·b_3_10 + c_4_16·b_1_08·b_1_1
       + c_4_16·b_1_09 + c_4_16·b_8_47·b_1_1 + b_4_15·c_8_49·b_1_3 + b_4_15·c_8_49·b_1_1
       + b_4_15·c_4_16·b_5_23 + b_4_15·c_4_16·b_1_15 + b_4_152·c_4_16·b_1_1
       + c_8_49·b_1_32·a_3_11 + c_8_49·a_1_2·b_1_14 + c_4_16·b_1_1·a_3_11·b_5_23
       + c_4_16·b_1_16·a_3_11 + c_4_16·b_8_47·a_1_2 + b_4_152·c_4_16·a_1_2
       + c_8_49·a_1_22·b_1_33 + c_4_16·a_1_2·b_1_35·a_3_11 + c_8_49·a_1_22·a_3_11
       + c_4_16·a_1_22·b_1_34·a_3_11 + c_4_162·b_1_02·b_3_10 + b_4_15·c_4_162·b_1_1
       + b_4_15·c_4_162·b_1_0 + c_4_162·b_1_32·a_3_11 + c_4_162·b_1_12·a_3_11
       + c_4_162·a_1_2·b_1_3·a_3_11 + c_4_162·a_1_22·a_3_11
  54. b_8_47·b_5_24 + b_8_47·b_1_15 + b_8_47·b_1_04·b_1_1 + b_1_310·a_3_11
       + b_1_110·a_3_11 + b_8_47·b_1_32·a_3_11 + b_8_47·a_1_2·b_1_34
       + b_8_47·a_1_2·b_1_14 + b_4_15·b_1_1·a_3_11·b_5_23 + b_4_15·a_1_2·b_1_13·b_5_23
       + b_4_153·a_1_2 + a_1_2·b_1_39·a_3_11 + c_8_49·b_1_14·b_1_3 + c_8_49·b_1_15
       + c_8_49·b_1_0·b_1_1·b_3_10 + c_4_16·b_1_39 + c_4_16·b_1_13·b_1_3·b_5_23
       + c_4_16·b_1_14·b_5_23 + c_4_16·b_1_19 + c_4_16·b_1_05·b_1_1·b_3_10
       + c_4_16·b_1_08·b_1_1 + c_4_16·b_8_47·b_1_0 + b_4_15·c_8_49·b_1_3
       + b_4_15·c_8_49·b_1_1 + b_4_15·c_4_16·b_5_23 + b_4_15·c_4_16·b_5_22
       + b_4_152·c_4_16·b_1_1 + c_8_49·b_1_32·a_3_11 + c_8_49·b_1_12·a_3_11
       + c_8_49·a_1_2·b_1_14 + c_4_16·b_1_3·a_3_11·b_5_24 + c_4_16·a_1_2·b_1_33·b_5_24
       + c_4_16·a_1_2·b_1_18 + b_4_15·c_8_49·a_1_2 + b_4_152·c_4_16·a_1_2
       + c_8_49·a_1_2·b_1_3·a_3_11 + c_4_16·a_1_2·b_1_35·a_3_11 + c_4_16·a_1_22·b_1_37
       + c_8_49·a_1_22·a_3_11 + c_4_162·b_1_14·b_1_3 + c_4_162·b_1_15
       + c_4_162·b_1_0·b_1_1·b_3_10 + c_4_162·b_1_04·b_1_1 + b_4_15·c_4_162·b_1_3
       + b_4_15·c_4_162·b_1_0 + c_4_162·b_1_32·a_3_11 + c_4_162·a_1_2·b_1_3·a_3_11
       + c_4_162·a_1_22·a_3_11
  55. b_7_402 + b_1_113·b_1_3 + b_8_47·b_1_16 + b_4_152·b_1_1·b_5_23 + b_1_111·a_3_11
       + b_4_15·b_1_17·a_3_11 + b_4_153·a_1_2·b_1_1 + c_8_49·b_1_15·b_1_3 + c_8_49·b_1_16
       + c_8_49·b_1_03·b_3_10 + c_4_16·b_1_19·b_1_3 + c_4_16·b_1_110
       + c_4_16·b_8_47·b_1_12 + b_4_15·c_4_16·b_1_3·b_5_23 + b_4_15·c_4_16·b_1_1·b_5_23
       + b_4_15·c_4_16·b_1_16 + b_4_152·c_4_16·b_1_12 + c_8_49·b_1_13·a_3_11
       + c_4_16·a_3_11·b_7_40 + b_4_15·c_8_49·a_1_2·b_1_1 + b_4_152·c_4_16·a_1_2·b_1_1
       + c_4_16·a_1_2·b_1_36·a_3_11 + c_4_16·a_1_22·b_1_38
       + c_4_16·a_1_22·a_3_11·b_5_24 + c_4_16·a_1_22·b_1_35·a_3_11
       + c_4_16·c_8_49·b_1_02 + c_4_162·b_1_15·b_1_3 + c_4_162·b_1_05·b_1_1
       + b_4_15·c_4_162·b_1_12 + c_4_162·a_3_11·b_3_10 + c_4_162·b_1_33·a_3_11
       + c_4_162·a_1_22·b_1_34 + c_4_162·a_1_22·b_1_3·a_3_11 + c_4_163·b_1_02
  56. b_8_47·b_7_40 + b_8_47·b_1_17 + b_8_47·a_1_2·b_1_16 + b_8_47·a_1_22·b_1_35
       + c_8_49·b_1_16·b_1_3 + c_8_49·b_1_17 + c_8_49·b_1_04·b_3_10
       + c_4_16·b_1_110·b_1_3 + c_4_16·b_1_111 + c_4_16·b_1_07·b_1_1·b_3_10
       + c_4_16·b_1_010·b_1_1 + c_4_16·b_8_47·b_3_10 + c_4_16·b_8_47·b_1_13
       + c_4_16·b_8_47·b_1_02·b_1_1 + b_4_15·c_8_49·b_1_12·b_1_3 + b_4_15·c_8_49·b_1_13
       + c_8_49·b_1_14·a_3_11 + c_8_49·a_1_2·b_1_16 + c_4_16·b_1_1·a_3_11·b_7_40
       + c_4_16·b_8_47·a_1_2·b_1_32 + b_4_15·c_8_49·a_1_2·b_1_12
       + b_4_15·c_4_16·a_1_2·b_1_1·b_5_23 + b_4_152·c_4_16·a_1_2·b_1_12
       + c_4_16·a_1_22·b_1_36·a_3_11 + c_4_16·c_8_49·b_1_02·b_1_1
       + c_4_16·c_8_49·b_1_03 + c_4_162·b_1_16·b_1_3 + c_4_162·b_1_17
       + c_4_162·b_1_02·b_5_23 + c_4_162·b_1_02·b_5_22 + c_4_162·b_1_06·b_1_1
       + b_4_15·c_4_162·b_1_12·b_1_3 + c_4_16·c_8_49·a_1_2·b_1_12
       + b_4_15·c_4_162·a_3_11 + c_4_162·a_1_2·b_1_33·a_3_11 + c_4_162·a_1_22·b_1_35
       + c_4_162·a_1_22·b_1_32·a_3_11 + c_4_162·a_1_23·b_1_3·a_3_11 + c_4_163·b_1_03
       + c_4_163·a_1_2·b_1_12 + c_4_163·a_1_22·b_1_3
  57. b_8_47·b_1_18 + b_8_472 + b_1_313·a_3_11 + b_1_113·a_3_11 + b_8_47·a_1_2·b_1_37
       + b_4_15·b_1_19·a_3_11 + a_1_2·b_1_312·a_3_11 + a_1_22·b_1_311·a_3_11
       + b_8_47·a_1_22·b_1_33·a_3_11 + c_8_49·b_1_17·b_1_3 + c_8_49·b_1_18
       + c_8_49·b_1_05·b_3_10 + c_4_16·b_1_312 + c_4_16·b_1_112 + c_4_16·b_8_47·b_1_14
       + b_4_15·c_4_16·b_1_12·b_1_3·b_5_23 + b_4_15·c_4_16·b_1_13·b_5_23
       + b_4_15·c_4_16·b_1_18 + b_4_152·c_8_49 + b_4_153·c_4_16 + c_8_49·b_1_15·a_3_11
       + b_4_15·c_8_49·a_1_2·b_1_13 + b_4_15·c_4_16·a_3_11·b_5_23
       + b_4_15·c_4_16·b_1_15·a_3_11 + b_4_152·c_4_16·a_1_2·b_1_13
       + c_8_49·a_1_2·b_1_34·a_3_11 + c_4_16·a_1_2·b_1_38·a_3_11
       + c_4_16·a_1_22·b_1_310 + c_4_16·a_1_22·b_1_37·a_3_11 + c_4_16·c_8_49·b_1_04
       + c_4_162·b_1_17·b_1_3 + c_4_162·b_1_18 + c_4_162·b_1_07·b_1_1
       + c_4_162·b_1_08 + b_4_15·c_4_162·b_1_14 + c_4_162·b_1_15·a_3_11
       + c_4_162·a_1_2·b_1_12·b_5_23 + b_4_15·c_4_162·a_1_2·b_1_13
       + c_4_16·c_8_49·a_1_22·b_1_32 + c_4_163·b_1_04 + c_4_163·a_1_23·b_1_3


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 16.
  • 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_16, a Duflot regular element of degree 4
    2. c_8_49, a Duflot regular element of degree 8
    3. b_1_32 + b_1_1·b_1_3 + b_1_12 + b_1_02, an element of degree 2
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 7, 11].
  • The filter degree type of any filter regular HSOP is [-1, -2, -3, -3].


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_20, an element of degree 1
  2. b_1_00, an element of degree 1
  3. b_1_10, an element of degree 1
  4. b_1_30, an element of degree 1
  5. a_3_110, an element of degree 3
  6. b_3_100, an element of degree 3
  7. b_4_150, an element of degree 4
  8. c_4_16c_1_04, an element of degree 4
  9. b_5_220, an element of degree 5
  10. b_5_230, an element of degree 5
  11. b_5_240, an element of degree 5
  12. b_7_400, an element of degree 7
  13. b_8_470, an element of degree 8
  14. c_8_49c_1_18 + c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_20, an element of degree 1
  2. b_1_0c_1_2, an element of degree 1
  3. b_1_10, an element of degree 1
  4. b_1_30, an element of degree 1
  5. a_3_110, an element of degree 3
  6. b_3_10c_1_0·c_1_22 + c_1_02·c_1_2, an element of degree 3
  7. b_4_150, an element of degree 4
  8. c_4_16c_1_0·c_1_23 + c_1_04, an element of degree 4
  9. b_5_22c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  10. b_5_23c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  11. b_5_24c_1_0·c_1_24 + c_1_04·c_1_2, an element of degree 5
  12. b_7_40c_1_0·c_1_12·c_1_24 + c_1_0·c_1_14·c_1_22 + c_1_02·c_1_25
       + c_1_02·c_1_12·c_1_23 + c_1_02·c_1_14·c_1_2 + c_1_04·c_1_23, an element of degree 7
  13. b_8_47c_1_0·c_1_27 + c_1_0·c_1_12·c_1_25 + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_26
       + c_1_02·c_1_12·c_1_24 + c_1_02·c_1_14·c_1_22, an element of degree 8
  14. c_8_49c_1_14·c_1_24 + c_1_18 + c_1_0·c_1_27 + c_1_02·c_1_26 + c_1_03·c_1_25
       + c_1_05·c_1_23 + c_1_06·c_1_22 + c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_20, an element of degree 1
  2. b_1_00, an element of degree 1
  3. b_1_1c_1_2, an element of degree 1
  4. b_1_30, an element of degree 1
  5. a_3_110, an element of degree 3
  6. b_3_100, an element of degree 3
  7. b_4_15c_1_0·c_1_23 + c_1_02·c_1_22, an element of degree 4
  8. c_4_16c_1_0·c_1_23 + c_1_04, an element of degree 4
  9. b_5_22c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  10. b_5_23c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_0·c_1_24 + c_1_02·c_1_23, an element of degree 5
  11. b_5_24c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  12. b_7_40c_1_12·c_1_25 + c_1_14·c_1_23, an element of degree 7
  13. b_8_47c_1_12·c_1_26 + c_1_14·c_1_24 + c_1_0·c_1_27 + c_1_0·c_1_12·c_1_25
       + c_1_0·c_1_14·c_1_23 + c_1_02·c_1_26 + c_1_02·c_1_12·c_1_24
       + c_1_02·c_1_14·c_1_22 + c_1_03·c_1_25 + c_1_04·c_1_24 + c_1_05·c_1_23
       + c_1_06·c_1_22, an element of degree 8
  14. c_8_49c_1_12·c_1_26 + c_1_18 + c_1_02·c_1_26 + c_1_03·c_1_25 + c_1_04·c_1_24
       + c_1_05·c_1_23 + c_1_06·c_1_22 + c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_20, an element of degree 1
  2. b_1_00, an element of degree 1
  3. b_1_10, an element of degree 1
  4. b_1_3c_1_2, an element of degree 1
  5. a_3_110, an element of degree 3
  6. b_3_100, an element of degree 3
  7. b_4_150, an element of degree 4
  8. c_4_16c_1_02·c_1_22 + c_1_04, an element of degree 4
  9. b_5_22c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  10. b_5_23c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  11. b_5_24c_1_0·c_1_24 + c_1_02·c_1_23, an element of degree 5
  12. b_7_400, an element of degree 7
  13. b_8_47c_1_0·c_1_27 + c_1_02·c_1_26, an element of degree 8
  14. c_8_49c_1_14·c_1_24 + c_1_18 + c_1_04·c_1_24 + c_1_08, an element of degree 8

Restriction map to a maximal el. ab. subgp. of rank 3

  1. a_1_20, an element of degree 1
  2. b_1_00, an element of degree 1
  3. b_1_1c_1_2, an element of degree 1
  4. b_1_3c_1_2, an element of degree 1
  5. a_3_110, an element of degree 3
  6. b_3_10c_1_23, an element of degree 3
  7. b_4_150, an element of degree 4
  8. c_4_16c_1_24 + c_1_02·c_1_22 + c_1_04, an element of degree 4
  9. b_5_220, an element of degree 5
  10. b_5_23c_1_12·c_1_23 + c_1_14·c_1_2 + c_1_02·c_1_23 + c_1_04·c_1_2, an element of degree 5
  11. b_5_24c_1_12·c_1_23 + c_1_14·c_1_2, an element of degree 5
  12. b_7_40c_1_02·c_1_25 + c_1_04·c_1_23, an element of degree 7
  13. b_8_470, an element of degree 8
  14. c_8_49c_1_12·c_1_26 + c_1_18 + c_1_04·c_1_24 + 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