Mod-3-Cohomology of group number 19 of order 162

About the group Ring generators Ring relations Completion information Restriction maps

General information on the group

  • The group order factors as 2 · 34.
  • It is non-abelian.
  • It has 3-Rank 3.
  • The centre of a Sylow 3-subgroup has rank 1.
  • Its Sylow 3-subgroup has 2 conjugacy classes of maximal elementary abelian subgroups, which are of rank 2 and 3, respectively.

Structure of the cohomology ring

The computation was based on 1 stability condition for H*(Syl3(A9); GF(3)).

General information

  • The cohomology ring is of dimension 3 and depth 2.
  • The depth exceeds the Duflot bound, which is 1.
  • The Poincaré series is
    ( − 1)·(1  −  2·t  +  2·t2  +  t3  −  2·t5  +  t6  +  t7  +  t8  −  2·t9  +  t10)
    ( − 1  +  t)3 · (1  +  t  +  t2) · (1  +  t2)2 · (1  −  t2  +  t4)
  • The a-invariants are -∞,-∞,-5,-3. They were obtained using the filter regular HSOP of the Hilbert-Poincaré test.
  • 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

Ring generators

The cohomology ring has 24 minimal generators of maximal degree 13:

  1. a_3_3, a nilpotent element of degree 3
  2. a_3_2, a nilpotent element of degree 3
  3. a_3_1, a nilpotent element of degree 3
  4. a_3_0, a nilpotent element of degree 3
  5. a_4_4, a nilpotent element of degree 4
  6. a_4_3, a nilpotent element of degree 4
  7. b_4_2, an element of degree 4
  8. b_4_1, an element of degree 4
  9. b_4_0, an element of degree 4
  10. a_5_1, a nilpotent element of degree 5
  11. a_5_0, a nilpotent element of degree 5
  12. a_6_1, a nilpotent element of degree 6
  13. b_6_0, an element of degree 6
  14. a_7_10, a nilpotent element of degree 7
  15. a_7_9, a nilpotent element of degree 7
  16. a_7_1, a nilpotent element of degree 7
  17. a_8_11, a nilpotent element of degree 8
  18. b_8_10, an element of degree 8
  19. b_8_9, an element of degree 8
  20. a_9_6, a nilpotent element of degree 9
  21. a_11_13, a nilpotent element of degree 11
  22. c_12_20, a Duflot element of degree 12
  23. a_12_16, a nilpotent element of degree 12
  24. a_13_10, a nilpotent element of degree 13

About the group Ring generators Ring relations Completion information Restriction maps

Ring relations

There are 12 "obvious" relations:
   a_3_02, a_3_12, a_3_22, a_3_32, a_5_02, a_5_12, a_7_12, a_7_92, a_7_102, a_9_62, a_11_132, a_13_102

Apart from that, there are 208 minimal relations of maximal degree 25:

  1. a_3_0·a_3_1
  2. a_3_0·a_3_3
  3. a_3_1·a_3_2
  4. a_3_2·a_3_3
  5. a_4_3·a_3_1
  6. a_4_3·a_3_3
  7. a_4_4·a_3_0 − a_4_3·a_3_2
  8. a_4_4·a_3_1
  9. a_4_4·a_3_2
  10. a_4_4·a_3_3
  11. b_4_0·a_3_1 − a_4_3·a_3_0
  12. b_4_0·a_3_3
  13. b_4_1·a_3_1 − a_4_3·a_3_2
  14. b_4_1·a_3_3
  15. b_4_2·a_3_0
  16. b_4_2·a_3_2
  17. a_4_32
  18. a_4_3·a_4_4
  19. a_4_42
  20. a_3_1·a_5_0
  21. a_3_1·a_5_1
  22. a_3_3·a_5_0
  23. a_3_3·a_5_1
  24. a_4_3·b_4_1 − a_3_2·a_5_0 + a_3_0·a_5_1
  25. a_4_3·b_4_2
  26. a_4_4·b_4_0 − a_3_2·a_5_0
  27. a_4_4·b_4_1 − a_3_2·a_5_1
  28. a_4_4·b_4_2
  29. b_4_0·b_4_2
  30. b_4_1·b_4_2
  31. a_4_3·a_5_1
  32. a_4_4·a_5_0
  33. a_4_4·a_5_1
  34. a_6_1·a_3_0 − a_4_3·a_5_0
  35. a_6_1·a_3_1
  36. a_6_1·a_3_2
  37. a_6_1·a_3_3
  38. b_4_2·a_5_0
  39. b_4_2·a_5_1
  40. b_6_0·a_3_1 − a_4_3·a_5_0
  41. b_6_0·a_3_2 − b_4_1·a_5_0 + b_4_0·a_5_1
  42. b_6_0·a_3_3
  43. a_4_3·a_6_1
  44. a_4_4·a_6_1
  45. a_3_0·a_7_10
  46. a_3_1·a_7_1
  47. a_3_1·a_7_9
  48. a_3_2·a_7_9
  49. a_3_2·a_7_10
  50. a_3_3·a_7_1
  51. a_3_3·a_7_9
  52. a_3_3·a_7_10
  53. a_5_0·a_5_1 − a_3_2·a_7_1 − b_4_0·a_3_0·a_3_2
  54. a_4_4·b_6_0 − a_3_2·a_7_1 − b_4_0·a_3_0·a_3_2
  55. b_4_0·a_6_1 − a_4_3·b_6_0 − a_3_0·a_7_1
  56. b_4_1·a_6_1 − a_3_2·a_7_1
  57. b_4_2·a_6_1
  58. b_4_2·b_6_0
  59. a_4_3·a_7_1
  60. a_4_3·a_7_10
  61. a_4_4·a_7_1 − a_3_0·a_3_2·a_5_0
  62. a_4_4·a_7_9
  63. a_4_4·a_7_10
  64. a_6_1·a_5_0 + a_4_3·b_4_0·a_3_0
  65. a_6_1·a_5_1 + a_3_0·a_3_2·a_5_0
  66. a_8_11·a_3_0 − a_4_3·a_7_9
  67. a_8_11·a_3_1
  68. a_8_11·a_3_2
  69. a_8_11·a_3_3
  70. b_4_0·a_7_10
  71. b_4_1·a_7_10
  72. b_4_2·a_7_1
  73. b_4_2·a_7_9
  74. b_6_0·a_5_0 + b_4_1·a_7_9 − b_4_0·a_7_1 − b_4_02·a_3_2 + b_4_02·a_3_0
  75. b_6_0·a_5_1 − b_4_1·a_7_1 + b_4_0·b_4_1·a_3_0 − b_4_02·a_3_2
  76. b_8_9·a_3_1 − a_4_3·a_7_9
  77. b_8_9·a_3_2 − b_4_1·a_7_9
  78. b_8_9·a_3_3
  79. b_8_10·a_3_0
  80. b_8_10·a_3_2
  81. b_8_10·a_3_3 − b_4_2·a_7_10
  82. a_4_3·a_8_11
  83. a_4_4·a_8_11
  84. a_6_12
  85. a_3_1·a_9_6
  86. a_3_3·a_9_6
  87. a_5_0·a_7_1 + a_3_2·a_9_6 − b_4_0·a_3_2·a_5_0 + b_4_0·a_3_0·a_5_0
  88. a_5_0·a_7_10
  89. a_5_1·a_7_1 − b_4_0·a_3_2·a_5_0 + b_4_0·a_3_0·a_5_1
  90. a_5_1·a_7_9 + a_3_2·a_9_6
  91. a_5_1·a_7_10
  92. a_4_3·b_8_9 + a_5_0·a_7_9 + a_3_0·a_9_6
  93. a_4_3·b_8_10
  94. a_4_4·b_8_9 − a_3_2·a_9_6
  95. a_4_4·b_8_10
  96. b_4_0·a_8_11 + a_5_0·a_7_9
  97. b_4_1·a_8_11 − a_3_2·a_9_6
  98. b_4_2·a_8_11
  99. a_6_1·b_6_0 + a_4_3·b_4_02 + a_3_2·a_9_6 − b_4_0·a_3_2·a_5_0 + b_4_0·a_3_0·a_5_0
  100. b_4_0·b_8_10
  101. b_4_1·b_8_10
  102. b_4_2·b_8_9
  103. b_6_02 + b_4_1·b_8_9 − b_4_02·b_4_1 + b_4_03
  104. a_4_3·a_9_6
  105. a_4_4·a_9_6
  106. a_6_1·a_7_1
  107. a_6_1·a_7_9
  108. a_6_1·a_7_10
  109. a_8_11·a_5_0
  110. a_8_11·a_5_1
  111. b_4_2·a_9_6
  112. b_6_0·a_7_1 + b_4_1·a_9_6 − b_4_0·b_6_0·a_3_0 − b_4_02·a_5_1 + b_4_02·a_5_0
  113. b_6_0·a_7_10
  114. b_8_9·a_5_0 − b_6_0·a_7_9 − b_4_0·a_9_6
  115. b_8_9·a_5_1 − b_4_1·a_9_6
  116. b_8_10·a_5_0
  117. b_8_10·a_5_1
  118. a_6_1·a_8_11
  119. a_3_1·a_11_13
  120. a_3_3·a_11_13
  121. a_5_0·a_9_6 − a_3_2·a_11_13 − b_4_0·a_3_0·a_7_9
  122. a_5_1·a_9_6
  123. a_7_1·a_7_9 + a_3_2·a_11_13
  124. a_7_1·a_7_10
  125. a_7_9·a_7_10
  126. a_6_1·b_8_9 − a_3_2·a_11_13
  127. a_6_1·b_8_10
  128. b_6_0·a_8_11 − a_3_2·a_11_13 − b_4_0·a_3_0·a_7_9
  129. b_6_0·b_8_10
  130. a_4_3·a_11_13
  131. a_4_4·a_11_13 + a_3_0·a_5_0·a_7_9
  132. a_6_1·a_9_6 − a_3_0·a_5_0·a_7_9
  133. a_8_11·a_7_1 + a_3_0·a_5_0·a_7_9
  134. a_8_11·a_7_9
  135. a_8_11·a_7_10
  136. a_12_16·a_3_0 + a_3_0·a_5_0·a_7_9
  137. a_12_16·a_3_1
  138. a_12_16·a_3_2 + a_3_0·a_5_0·a_7_9
  139. a_12_16·a_3_3
  140. b_4_2·a_11_13
  141. b_6_0·a_9_6 − b_4_1·a_11_13 + b_4_0·b_8_9·a_3_0 − b_4_02·a_7_9
  142. b_8_9·a_7_1 − b_4_1·a_11_13
  143. b_8_9·a_7_9 − c_12_20·a_3_2
  144. b_8_9·a_7_10
  145. b_8_10·a_7_1
  146. b_8_10·a_7_9
  147. b_8_10·a_7_10 − c_12_20·a_3_3
  148. a_4_3·a_12_16
  149. a_4_4·a_12_16
  150. a_8_112
  151. a_3_1·a_13_10
  152. a_3_2·a_13_10 + b_6_0·a_3_0·a_7_9 − b_4_0·a_5_0·a_7_9 − b_4_0·a_3_2·a_9_6
  153. a_3_3·a_13_10
  154. a_5_0·a_11_13 − a_3_0·a_13_10 + b_4_0·a_5_0·a_7_9 + b_4_0·a_3_0·a_9_6 + a_4_4·c_12_20
  155. a_5_1·a_11_13 + b_4_0·a_5_0·a_7_9 + b_4_0·a_3_0·a_9_6
  156. a_7_1·a_9_6 − b_4_0·a_5_0·a_7_9 − b_4_0·a_3_0·a_9_6
  157. a_7_9·a_9_6 − a_4_4·c_12_20
  158. a_7_10·a_9_6
  159. b_4_0·a_12_16 − a_3_0·a_13_10 + b_4_0·a_5_0·a_7_9 + b_4_0·a_3_0·a_9_6
  160. b_4_1·a_12_16 + b_6_0·a_3_0·a_7_9 − b_4_0·a_3_2·a_9_6 + b_4_0·a_3_0·a_9_6
  161. b_4_2·a_12_16
  162. a_8_11·b_8_9 − a_4_4·c_12_20
  163. a_8_11·b_8_10
  164. b_8_92 − b_4_1·c_12_20
  165. b_8_9·b_8_10
  166. b_8_102 − b_4_2·c_12_20
  167. a_4_3·a_13_10
  168. a_4_4·a_13_10 − a_3_0·a_3_2·a_11_13
  169. a_6_1·a_11_13
  170. a_8_11·a_9_6
  171. a_12_16·a_5_0
  172. a_12_16·a_5_1 + a_3_0·a_3_2·a_11_13
  173. b_4_2·a_13_10
  174. b_6_0·b_8_9·a_3_0 − b_4_1·a_13_10 − b_4_0·b_6_0·a_7_9 + b_4_0·b_4_1·a_9_6
       − b_4_02·a_9_6
  175. b_6_0·a_11_13 − b_4_0·a_13_10 + c_12_20·a_5_1
  176. b_8_9·a_9_6 − c_12_20·a_5_1
  177. b_8_10·a_9_6
  178. a_6_1·a_12_16
  179. a_5_0·a_13_10 − b_4_0·a_3_2·a_11_13 + b_4_0·a_3_0·a_11_13 − c_12_20·a_3_0·a_3_2
  180. a_5_1·a_13_10 + b_4_1·a_3_0·a_11_13 − b_4_0·a_3_2·a_11_13
  181. a_7_1·a_11_13
  182. a_7_9·a_11_13 − a_6_1·c_12_20
  183. a_7_10·a_11_13
  184. b_6_0·a_12_16 − b_4_0·a_3_2·a_11_13 + b_4_0·a_3_0·a_11_13 − c_12_20·a_3_0·a_3_2
  185. a_6_1·a_13_10 + a_4_3·c_12_20·a_3_2
  186. a_8_11·a_11_13 − a_4_3·c_12_20·a_3_0
  187. a_12_16·a_7_1 − a_4_3·c_12_20·a_3_2
  188. a_12_16·a_7_9 − a_4_3·c_12_20·a_3_0
  189. a_12_16·a_7_10
  190. b_6_0·a_13_10 − b_4_0·b_4_1·a_11_13 + b_4_02·a_11_13 + b_4_1·c_12_20·a_3_0
       − b_4_0·c_12_20·a_3_2
  191. b_8_9·a_11_13 − c_12_20·a_7_1
  192. b_8_10·a_11_13
  193. a_8_11·a_12_16
  194. a_7_1·a_13_10 + c_12_20·a_3_2·a_5_0 − c_12_20·a_3_0·a_5_1
  195. a_7_9·a_13_10 + a_4_3·b_4_0·c_12_20 − c_12_20·a_3_2·a_5_0 + c_12_20·a_3_0·a_5_0
  196. a_7_10·a_13_10
  197. a_9_6·a_11_13 − a_4_3·b_4_0·c_12_20
  198. b_8_9·a_12_16 − c_12_20·a_3_2·a_5_0 + c_12_20·a_3_0·a_5_0
  199. b_8_10·a_12_16
  200. a_8_11·a_13_10 − a_4_3·c_12_20·a_5_0
  201. a_12_16·a_9_6 + a_4_3·c_12_20·a_5_0
  202. b_8_9·a_13_10 − b_6_0·c_12_20·a_3_0 − b_4_0·c_12_20·a_5_1 + b_4_0·c_12_20·a_5_0
  203. b_8_10·a_13_10
  204. a_9_6·a_13_10 − a_4_3·b_6_0·c_12_20
  205. a_12_16·a_11_13 − a_4_3·c_12_20·a_7_9
  206. a_12_162
  207. a_11_13·a_13_10 − c_12_20·a_5_0·a_7_9 − c_12_20·a_3_0·a_9_6
  208. a_12_16·a_13_10

About the group Ring generators Ring relations Completion information Restriction maps

Data used for the Hilbert-Poincaré test

  • We proved completion in degree 25 using the Hilbert-Poincaré criterion.
  • 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_12_20, an element of degree 12
    2.  − b_4_23 + b_4_1·b_8_9 − b_4_13 − b_4_02·b_4_1 + b_4_03, an element of degree 12
    3. b_4_1, an element of degree 4
  • A Duflot regular sequence is given by c_12_20.
  • The Raw Filter Degree Type of the filter regular HSOP is [-1, -1, 19, 25].
  • Modifying the above filter regular HSOP, we obtained the following parameters:
    1. c_12_20, an element of degree 12
    2. b_4_2 + b_4_0, an element of degree 4
    3. b_4_1, an element of degree 4

About the group Ring generators Ring relations Completion information Restriction maps

Restriction maps

Expressing the generators as elements of H*(Syl3(A9); GF(3))

  1. a_3_3 → b_2_0·a_1_0
  2. a_3_2 → b_2_2·a_1_1
  3. a_3_1 → a_3_3
  4. a_3_0 → a_3_4
  5. a_4_4 → a_1_1·a_3_2
  6. a_4_3 → a_4_5
  7. b_4_2 → b_2_02
  8. b_4_1 → b_2_22
  9. b_4_0 → b_4_6
  10. a_5_1 → b_2_2·a_3_2
  11. a_5_0 → a_5_7 − b_4_6·a_1_1
  12. a_6_1 → a_1_1·a_5_8
  13. b_6_0 → b_6_10 − b_2_2·b_4_6
  14. a_7_10 → c_6_11·a_1_0
  15. a_7_9 → c_6_11·a_1_1
  16. a_7_1 → b_2_2·a_5_8
  17. a_8_11 → a_2_1·c_6_11
  18. b_8_10 → b_2_0·c_6_11
  19. b_8_9 → b_2_2·c_6_11
  20. a_9_6 → c_6_11·a_3_2
  21. a_11_13 → c_6_11·a_5_8
  22. c_12_20 → c_6_112
  23. a_12_16 → a_6_9·c_6_11 − c_6_11·a_1_1·a_5_8
  24. a_13_10 → c_6_11·a_7_14 − b_2_2·c_6_11·a_5_8

Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 1

  1. a_3_3 → 0, an element of degree 3
  2. a_3_2 → 0, an element of degree 3
  3. a_3_1 → 0, an element of degree 3
  4. a_3_0 → 0, an element of degree 3
  5. a_4_4 → 0, an element of degree 4
  6. a_4_3 → 0, an element of degree 4
  7. b_4_2 → 0, an element of degree 4
  8. b_4_1 → 0, an element of degree 4
  9. b_4_0 → 0, an element of degree 4
  10. a_5_1 → 0, an element of degree 5
  11. a_5_0 → 0, an element of degree 5
  12. a_6_1 → 0, an element of degree 6
  13. b_6_0 → 0, an element of degree 6
  14. a_7_10 → 0, an element of degree 7
  15. a_7_9 → 0, an element of degree 7
  16. a_7_1 → 0, an element of degree 7
  17. a_8_11 → 0, an element of degree 8
  18. b_8_10 → 0, an element of degree 8
  19. b_8_9 → 0, an element of degree 8
  20. a_9_6 → 0, an element of degree 9
  21. a_11_13 → 0, an element of degree 11
  22. c_12_20 → c_2_06, an element of degree 12
  23. a_12_16 → 0, an element of degree 12
  24. a_13_10 → 0, an element of degree 13

Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup

  1. a_3_3 → c_2_2·a_1_1, an element of degree 3
  2. a_3_2 → 0, an element of degree 3
  3. a_3_1 →  − c_2_2·a_1_0 + c_2_1·a_1_1, an element of degree 3
  4. a_3_0 → 0, an element of degree 3
  5. a_4_4 → 0, an element of degree 4
  6. a_4_3 → 0, an element of degree 4
  7. b_4_2 → c_2_22, an element of degree 4
  8. b_4_1 → 0, an element of degree 4
  9. b_4_0 → 0, an element of degree 4
  10. a_5_1 → 0, an element of degree 5
  11. a_5_0 → 0, an element of degree 5
  12. a_6_1 → 0, an element of degree 6
  13. b_6_0 → 0, an element of degree 6
  14. a_7_10 →  − c_2_1·c_2_22·a_1_1 + c_2_13·a_1_1, an element of degree 7
  15. a_7_9 → 0, an element of degree 7
  16. a_7_1 → 0, an element of degree 7
  17. a_8_11 → 0, an element of degree 8
  18. b_8_10 →  − c_2_1·c_2_23 + c_2_13·c_2_2, an element of degree 8
  19. b_8_9 → 0, an element of degree 8
  20. a_9_6 → 0, an element of degree 9
  21. a_11_13 → 0, an element of degree 11
  22. c_12_20 → c_2_12·c_2_24 + c_2_14·c_2_22 + c_2_16, an element of degree 12
  23. a_12_16 → 0, an element of degree 12
  24. a_13_10 → 0, an element of degree 13

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

  1. a_3_3 → 0, an element of degree 3
  2. a_3_2 → c_2_4·a_1_1, an element of degree 3
  3. a_3_1 →  − a_1_0·a_1_1·a_1_2, an element of degree 3
  4. a_3_0 →  − c_2_5·a_1_2 − c_2_5·a_1_1 − c_2_4·a_1_2 + c_2_4·a_1_0 + c_2_3·a_1_1, an element of degree 3
  5. a_4_4 →  − c_2_4·a_1_1·a_1_2, an element of degree 4
  6. a_4_3 →  − c_2_5·a_1_0·a_1_1 + c_2_4·a_1_0·a_1_2 − c_2_3·a_1_1·a_1_2, an element of degree 4
  7. b_4_2 → 0, an element of degree 4
  8. b_4_1 → c_2_42, an element of degree 4
  9. b_4_0 →  − c_2_52 + c_2_4·c_2_5 − c_2_3·c_2_4, an element of degree 4
  10. a_5_1 → c_2_4·c_2_5·a_1_1 − c_2_42·a_1_2, an element of degree 5
  11. a_5_0 → c_2_52·a_1_2 + c_2_52·a_1_1 − c_2_4·c_2_5·a_1_2 − c_2_4·c_2_5·a_1_1
       − c_2_3·c_2_5·a_1_1 + c_2_3·c_2_4·a_1_2, an element of degree 5
  12. a_6_1 → c_2_52·a_1_0·a_1_1 − c_2_4·c_2_5·a_1_0·a_1_1 + c_2_3·c_2_5·a_1_1·a_1_2
       + c_2_3·c_2_4·a_1_1·a_1_2 + c_2_3·c_2_4·a_1_0·a_1_1, an element of degree 6
  13. b_6_0 → c_2_53 − c_2_42·c_2_5, an element of degree 6
  14. a_7_10 → 0, an element of degree 7
  15. a_7_9 →  − c_2_3·c_2_52·a_1_1 + c_2_3·c_2_4·c_2_5·a_1_1 + c_2_32·c_2_4·a_1_1 + c_2_33·a_1_1, an element of degree 7
  16. a_7_1 →  − c_2_4·c_2_52·a_1_0 + c_2_42·c_2_5·a_1_0 + c_2_3·c_2_4·c_2_5·a_1_2
       + c_2_3·c_2_4·c_2_5·a_1_1 + c_2_3·c_2_42·a_1_2 − c_2_3·c_2_42·a_1_0
       + c_2_32·c_2_4·a_1_1, an element of degree 7
  17. a_8_11 → c_2_3·c_2_52·a_1_1·a_1_2 − c_2_3·c_2_4·c_2_5·a_1_1·a_1_2
       − c_2_32·c_2_4·a_1_1·a_1_2 − c_2_33·a_1_1·a_1_2, an element of degree 8
  18. b_8_10 → 0, an element of degree 8
  19. b_8_9 →  − c_2_3·c_2_4·c_2_52 + c_2_3·c_2_42·c_2_5 + c_2_32·c_2_42 + c_2_33·c_2_4, an element of degree 8
  20. a_9_6 →  − c_2_3·c_2_53·a_1_1 + c_2_3·c_2_4·c_2_52·a_1_2 + c_2_3·c_2_4·c_2_52·a_1_1
       − c_2_3·c_2_42·c_2_5·a_1_2 + c_2_32·c_2_4·c_2_5·a_1_1 − c_2_32·c_2_42·a_1_2
       + c_2_33·c_2_5·a_1_1 − c_2_33·c_2_4·a_1_2, an element of degree 9
  21. a_11_13 → c_2_3·c_2_54·a_1_0 + c_2_3·c_2_4·c_2_53·a_1_0 + c_2_3·c_2_42·c_2_52·a_1_0
       − c_2_32·c_2_53·a_1_2 − c_2_32·c_2_53·a_1_1 + c_2_32·c_2_4·c_2_52·a_1_1
       + c_2_32·c_2_42·c_2_5·a_1_2 − c_2_33·c_2_52·a_1_1 − c_2_33·c_2_52·a_1_0
       + c_2_33·c_2_4·c_2_5·a_1_2 − c_2_33·c_2_4·c_2_5·a_1_1 + c_2_33·c_2_4·c_2_5·a_1_0
       + c_2_33·c_2_42·a_1_2 − c_2_33·c_2_42·a_1_0 + c_2_34·c_2_5·a_1_2
       + c_2_34·c_2_5·a_1_1 + c_2_34·c_2_4·a_1_2 + c_2_34·c_2_4·a_1_1 − c_2_34·c_2_4·a_1_0
       + c_2_35·a_1_1, an element of degree 11
  22. c_12_20 → c_2_32·c_2_54 + c_2_32·c_2_4·c_2_53 + c_2_32·c_2_42·c_2_52
       + c_2_33·c_2_4·c_2_52 − c_2_33·c_2_42·c_2_5 + c_2_34·c_2_52
       − c_2_34·c_2_4·c_2_5 + c_2_34·c_2_42 − c_2_35·c_2_4 + c_2_36, an element of degree 12
  23. a_12_16 → c_2_3·c_2_54·a_1_0·a_1_2 + c_2_3·c_2_54·a_1_0·a_1_1
       + c_2_3·c_2_4·c_2_53·a_1_0·a_1_2 + c_2_3·c_2_4·c_2_53·a_1_0·a_1_1
       + c_2_3·c_2_42·c_2_52·a_1_0·a_1_2 + c_2_3·c_2_42·c_2_52·a_1_0·a_1_1
       − c_2_32·c_2_53·a_1_0·a_1_1 − c_2_32·c_2_4·c_2_52·a_1_1·a_1_2
       + c_2_32·c_2_42·c_2_5·a_1_1·a_1_2 + c_2_32·c_2_42·c_2_5·a_1_0·a_1_1
       + c_2_33·c_2_52·a_1_1·a_1_2 − c_2_33·c_2_52·a_1_0·a_1_2
       − c_2_33·c_2_52·a_1_0·a_1_1 − c_2_33·c_2_4·c_2_5·a_1_1·a_1_2
       + c_2_33·c_2_4·c_2_5·a_1_0·a_1_2 − c_2_33·c_2_4·c_2_5·a_1_0·a_1_1
       + c_2_33·c_2_42·a_1_1·a_1_2 − c_2_33·c_2_42·a_1_0·a_1_2
       + c_2_34·c_2_5·a_1_0·a_1_1 − c_2_34·c_2_4·a_1_0·a_1_2 − c_2_35·a_1_1·a_1_2, an element of degree 12
  24. a_13_10 →  − c_2_3·c_2_55·a_1_0 + c_2_3·c_2_4·c_2_54·a_1_0 + c_2_3·c_2_42·c_2_53·a_1_0
       − c_2_3·c_2_43·c_2_52·a_1_0 + c_2_32·c_2_54·a_1_2 + c_2_32·c_2_54·a_1_1
       + c_2_32·c_2_4·c_2_53·a_1_2 − c_2_32·c_2_4·c_2_53·a_1_1
       + c_2_32·c_2_4·c_2_53·a_1_0 + c_2_32·c_2_43·c_2_5·a_1_2
       − c_2_32·c_2_43·c_2_5·a_1_0 + c_2_33·c_2_53·a_1_1 + c_2_33·c_2_53·a_1_0
       + c_2_33·c_2_4·c_2_52·a_1_2 + c_2_33·c_2_4·c_2_52·a_1_1
       − c_2_33·c_2_42·c_2_5·a_1_2 − c_2_33·c_2_42·c_2_5·a_1_0 + c_2_33·c_2_43·a_1_2
       − c_2_34·c_2_52·a_1_2 − c_2_34·c_2_52·a_1_1 + c_2_34·c_2_4·c_2_5·a_1_2
       − c_2_34·c_2_4·c_2_5·a_1_1 − c_2_34·c_2_42·a_1_2 − c_2_35·c_2_5·a_1_1
       + c_2_35·c_2_4·a_1_2, an element of degree 13

About the group Ring generators Ring relations Completion information Restriction maps


Simon King
Department of Mathematics and Computer Science
Friedrich-Schiller-Universität Jena
07737 Jena
GERMANY
E-mail: simon dot king at uni hyphen jena dot de
Tel: +49 (0)3641 9-46161
Fax: +49 (0)3641 9-46162
Office: Zi. 3529, Ernst-Abbe-Platz 2

Last change: 14.12.2010