Cohomology of group number 9 of order 243

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243

General information on the group

  • The group has 2 minimal generators and exponent 9.
  • It is non-abelian.
  • It has p-Rank 3.
  • Its center has rank 2.
  • It has a unique conjugacy class of maximal elementary abelian subgroups, which is 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
    t8  −  t4  +  t3  −  2·t2  +  t  −  1
    (t  −  1)3 · (t2  −  t  +  1)2 · (t2  +  t  +  1)2
  • The a-invariants are -∞,-∞,-3,-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 243

Ring generators

The cohomology ring has 30 minimal generators of maximal degree 8:

  1. a_1_0, a nilpotent element of degree 1
  2. a_1_1, a nilpotent element of degree 1
  3. a_2_0, a nilpotent element of degree 2
  4. a_2_1, a nilpotent element of degree 2
  5. a_2_2, a nilpotent element of degree 2
  6. a_3_1, a nilpotent element of degree 3
  7. a_3_2, a nilpotent element of degree 3
  8. a_3_3, a nilpotent element of degree 3
  9. a_3_4, a nilpotent element of degree 3
  10. a_4_2, a nilpotent element of degree 4
  11. a_4_3, a nilpotent element of degree 4
  12. a_4_4, a nilpotent element of degree 4
  13. b_4_5, an element of degree 4
  14. a_5_2, a nilpotent element of degree 5
  15. a_5_3, a nilpotent element of degree 5
  16. a_5_4, a nilpotent element of degree 5
  17. a_5_5, a nilpotent element of degree 5
  18. a_5_6, a nilpotent element of degree 5
  19. a_6_3, a nilpotent element of degree 6
  20. a_6_4, a nilpotent element of degree 6
  21. a_6_5, a nilpotent element of degree 6
  22. a_6_6, a nilpotent element of degree 6
  23. b_6_7, an element of degree 6
  24. c_6_8, a Duflot regular element of degree 6
  25. c_6_9, a Duflot regular element of degree 6
  26. a_7_8, a nilpotent element of degree 7
  27. a_7_9, a nilpotent element of degree 7
  28. a_7_10, a nilpotent element of degree 7
  29. a_7_11, a nilpotent element of degree 7
  30. a_8_11, a nilpotent element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243

Ring relations

There are 15 "obvious" relations:
   a_1_02, a_1_12, a_3_12, a_3_22, a_3_32, a_3_42, a_5_22, a_5_32, a_5_42, a_5_52, a_5_62, a_7_82, a_7_92, a_7_102, a_7_112

Apart from that, there are 360 minimal relations of maximal degree 16:

  1. a_1_0·a_1_1
  2. a_2_0·a_1_1
  3. a_2_1·a_1_1 + a_2_0·a_1_0
  4. a_2_1·a_1_0 − a_2_0·a_1_0
  5. a_2_2·a_1_1 − a_2_0·a_1_0
  6. a_2_2·a_1_0 − a_2_0·a_1_0
  7. a_2_02
  8. a_2_0·a_2_1
  9. a_2_12
  10.  − a_2_22 + a_2_1·a_2_2 + a_2_0·a_2_2
  11. a_1_1·a_3_1 − a_2_22 − a_2_0·a_2_2
  12. a_1_0·a_3_1 − a_2_0·a_2_2
  13. a_1_1·a_3_2 + a_2_22 − a_2_0·a_2_2
  14. a_1_0·a_3_2 − a_2_22
  15. a_1_1·a_3_3
  16. a_1_0·a_3_3
  17. a_1_1·a_3_4 + a_2_22 + a_2_0·a_2_2
  18. a_1_0·a_3_4 − a_2_0·a_2_2
  19. a_2_2·a_3_1
  20. a_2_0·a_3_1
  21. a_2_1·a_3_1
  22. a_2_2·a_3_2
  23. a_2_0·a_3_2
  24. a_2_1·a_3_2
  25. a_2_2·a_3_3 + a_2_1·a_3_3 + a_2_0·a_3_3
  26. a_2_2·a_3_4 + a_2_0·a_3_3
  27. a_2_2·a_3_3 + a_2_0·a_3_4 + a_2_0·a_3_3
  28.  − a_2_2·a_3_3 + a_2_1·a_3_4 + a_2_0·a_3_3
  29. a_4_2·a_1_1 + a_2_2·a_3_3 − a_2_0·a_3_3
  30. a_4_2·a_1_0 − a_2_0·a_3_3
  31. a_4_3·a_1_1 + a_2_0·a_3_3
  32. a_4_3·a_1_0 + a_2_2·a_3_3 − a_2_0·a_3_3
  33. a_4_4·a_1_1 − a_2_2·a_3_3 + a_2_0·a_3_3
  34. a_4_4·a_1_0 + a_2_0·a_3_3
  35. b_4_5·a_1_1 − a_2_2·a_3_3 + a_2_0·a_3_3
  36. b_4_5·a_1_0 − a_2_0·a_3_3
  37. a_3_1·a_3_2
  38. a_3_2·a_3_4 − a_3_1·a_3_3
  39.  − a_3_2·a_3_3 + a_3_1·a_3_4 + a_3_1·a_3_3
  40. a_3_1·a_3_3 + a_2_2·a_4_2
  41. a_2_0·a_4_2
  42. a_2_1·a_4_2
  43. a_3_2·a_3_3 + a_3_1·a_3_3 + a_2_2·a_4_3
  44. a_2_0·a_4_3
  45. a_2_1·a_4_3
  46.  − a_3_1·a_3_3 + a_2_2·a_4_4
  47. a_2_0·a_4_4
  48. a_2_1·a_4_4
  49. a_2_2·b_4_5 − a_3_3·a_3_4
  50. a_2_0·b_4_5
  51. a_2_1·b_4_5
  52. a_1_1·a_5_2
  53. a_1_0·a_5_2
  54. a_3_2·a_3_3 + a_3_1·a_3_3 + a_1_1·a_5_3
  55. a_3_1·a_3_3 + a_1_0·a_5_3
  56. a_3_1·a_3_3 + a_1_1·a_5_4
  57.  − a_3_2·a_3_3 − a_3_1·a_3_3 + a_1_0·a_5_4
  58. a_3_3·a_3_4 + a_3_2·a_3_3 + a_1_1·a_5_5
  59.  − a_3_2·a_3_3 + a_1_0·a_5_5
  60. a_3_3·a_3_4 − a_3_1·a_3_3 + a_1_1·a_5_6
  61. a_3_3·a_3_4 − a_3_2·a_3_3 + a_3_1·a_3_3 + a_1_0·a_5_6
  62. a_4_2·a_3_1
  63. a_4_3·a_3_3 − a_4_2·a_3_4 + a_4_2·a_3_3
  64. a_4_3·a_3_2 + a_4_2·a_3_2
  65. a_4_3·a_3_1 − a_4_2·a_3_2
  66. a_4_3·a_3_4 − a_4_2·a_3_4 − a_4_2·a_3_3 − a_4_2·a_3_2
  67. a_4_4·a_3_3 + a_4_2·a_3_3 + a_4_2·a_3_2
  68. a_4_4·a_3_2 + a_4_2·a_3_2
  69. a_4_4·a_3_1
  70. a_4_4·a_3_4 + a_4_2·a_3_4 + a_4_2·a_3_2
  71. b_4_5·a_3_2
  72. b_4_5·a_3_1
  73. b_4_5·a_3_4 − b_4_5·a_3_3
  74.  − a_4_2·a_3_2 + a_2_2·a_5_2
  75. a_2_0·a_5_2
  76. a_2_1·a_5_2
  77. a_2_2·a_5_3
  78. a_2_0·a_5_3
  79.  − a_4_2·a_3_2 + a_2_1·a_5_3
  80. a_4_2·a_3_2 + a_2_2·a_5_4
  81. a_4_2·a_3_2 + a_2_0·a_5_4
  82. a_4_2·a_3_2 + a_2_1·a_5_4
  83. a_4_2·a_3_4 + a_4_2·a_3_3 − a_4_2·a_3_2 + a_2_2·a_5_5
  84.  − a_4_2·a_3_3 + a_4_2·a_3_2 + a_2_0·a_5_5
  85.  − a_4_2·a_3_4 + a_2_1·a_5_5
  86. a_4_2·a_3_3 + a_4_2·a_3_2 + a_2_2·a_5_6
  87.  − a_4_2·a_3_4 + a_4_2·a_3_2 + a_2_0·a_5_6
  88. a_4_2·a_3_4 − a_4_2·a_3_3 − a_4_2·a_3_2 + a_2_1·a_5_6
  89. a_6_3·a_1_1 − a_4_2·a_3_4 + a_4_2·a_3_3
  90. a_6_3·a_1_0 − a_4_2·a_3_3
  91. a_6_4·a_1_1 + a_4_2·a_3_4
  92. a_6_4·a_1_0 − a_4_2·a_3_4 − a_4_2·a_3_3
  93. a_6_5·a_1_1 + a_4_2·a_3_4 − a_4_2·a_3_3 − a_4_2·a_3_2
  94. a_6_5·a_1_0 + a_4_2·a_3_3
  95. a_6_6·a_1_1 + a_4_2·a_3_3 − a_4_2·a_3_2
  96. a_6_6·a_1_0 − a_4_2·a_3_4 + a_4_2·a_3_3 − a_4_2·a_3_2
  97. b_6_7·a_1_1 − a_4_2·a_3_3 − a_4_2·a_3_2
  98. b_6_7·a_1_0 + a_4_2·a_3_4 − a_4_2·a_3_3 − a_4_2·a_3_2
  99. a_4_32 + a_4_22
  100. a_4_2·a_4_3
  101. a_4_3·a_4_4
  102. a_4_42 − a_4_22
  103. a_4_2·a_4_4 + a_4_22
  104. a_4_3·b_4_5
  105. a_4_4·b_4_5 − a_4_22
  106. a_4_2·b_4_5 − a_4_22
  107. a_3_3·a_5_2
  108. a_3_2·a_5_2
  109. a_3_1·a_5_2
  110. a_3_4·a_5_2 + a_4_22
  111. a_3_2·a_5_3
  112. a_3_1·a_5_3
  113. a_3_4·a_5_3 + a_3_3·a_5_4 − a_3_3·a_5_3 + a_4_22
  114. a_3_2·a_5_4
  115. a_3_1·a_5_4
  116. a_3_4·a_5_4 + a_3_4·a_5_3 + a_3_3·a_5_3 + a_4_22
  117. a_3_4·a_5_3 + a_3_3·a_5_3 + a_3_2·a_5_5 + a_4_22
  118. a_3_3·a_5_3 + a_3_1·a_5_5
  119. a_3_4·a_5_5 − a_3_4·a_5_3 − a_3_3·a_5_5 + a_3_3·a_5_3 − a_4_22
  120. a_3_3·a_5_3 + a_3_2·a_5_6
  121. a_3_4·a_5_3 + a_3_1·a_5_6 + a_4_22
  122. a_3_4·a_5_6 − a_3_4·a_5_3 − a_3_3·a_5_6 + a_3_3·a_5_3 + a_4_22
  123.  − a_3_3·a_5_3 − a_4_22 + a_2_2·a_6_3
  124.  − a_4_22 + a_2_0·a_6_3
  125.  − a_4_22 + a_2_1·a_6_3
  126.  − a_3_4·a_5_3 − a_3_3·a_5_3 − a_4_22 + a_2_2·a_6_4
  127. a_4_22 + a_2_0·a_6_4
  128.  − a_4_22 + a_2_1·a_6_4
  129. a_3_3·a_5_3 + a_4_22 + a_2_2·a_6_5
  130. a_4_22 + a_2_0·a_6_5
  131. a_4_22 + a_2_1·a_6_5
  132.  − a_3_4·a_5_3 + a_3_3·a_5_3 + a_4_22 + a_2_2·a_6_6
  133. a_2_0·a_6_6
  134. a_4_22 + a_2_1·a_6_6
  135. a_2_2·b_6_7 + a_3_4·a_5_3 − a_3_3·a_5_3
  136. a_2_0·b_6_7
  137. a_2_1·b_6_7 − a_4_22
  138.  − a_3_4·a_5_3 + a_3_3·a_5_3 + a_1_1·a_7_8 − a_4_22
  139.  − a_3_3·a_5_3 + a_1_0·a_7_8
  140.  − a_3_3·a_5_3 + a_1_1·a_7_9
  141. a_3_4·a_5_3 − a_3_3·a_5_3 + a_1_0·a_7_9 + a_4_22
  142.  − a_3_4·a_5_3 + a_3_3·a_5_3 + a_1_1·a_7_10
  143.  − a_3_3·a_5_3 + a_1_0·a_7_10
  144.  − a_3_3·a_5_3 + a_1_1·a_7_11 − a_4_22
  145. a_3_4·a_5_3 − a_3_3·a_5_3 + a_1_0·a_7_11 − a_4_22
  146. a_4_3·a_5_2
  147. a_4_4·a_5_2
  148. a_4_2·a_5_2
  149. b_4_5·a_5_3 − b_4_5·a_5_2 + a_4_4·a_5_3
  150. a_4_4·a_5_3 + a_4_2·a_5_3
  151. a_4_4·a_5_3 + a_4_3·a_5_4
  152. a_4_4·a_5_4 − a_4_3·a_5_3
  153. b_4_5·a_5_4 − a_4_3·a_5_3
  154. a_4_3·a_5_3 + a_4_2·a_5_4
  155. a_4_4·a_5_5 + a_4_3·a_5_3 + a_4_2·a_5_5
  156.  − a_4_4·a_5_5 + a_4_4·a_5_3 + a_4_3·a_5_6 − a_4_3·a_5_5 + a_4_3·a_5_3
  157. a_4_4·a_5_6 − a_4_4·a_5_5 − a_4_4·a_5_3 + a_4_3·a_5_5 − a_4_3·a_5_3
  158. a_4_4·a_5_5 − a_4_4·a_5_3 − a_4_3·a_5_5 − a_4_3·a_5_3 + a_4_2·a_5_6
  159. a_4_4·a_5_5 − a_4_4·a_5_3 + a_2_0·c_6_8·a_1_0
  160. a_4_4·a_5_5 + a_4_4·a_5_3 − a_4_3·a_5_5 + a_4_3·a_5_3 + a_2_0·c_6_9·a_1_0
  161. a_6_3·a_3_3 + a_4_4·a_5_5 − a_4_4·a_5_3
  162. a_6_3·a_3_2 − a_4_4·a_5_3 − a_4_3·a_5_3
  163. a_6_3·a_3_1 + a_4_4·a_5_3
  164. a_6_3·a_3_4 + a_4_4·a_5_5 − a_4_4·a_5_3 − a_4_3·a_5_5 + a_4_3·a_5_3
  165. a_6_4·a_3_3 − a_4_4·a_5_5 − a_4_3·a_5_5 + a_4_3·a_5_3
  166. a_6_4·a_3_2 − a_4_3·a_5_3
  167. a_6_4·a_3_1 − a_4_4·a_5_3 − a_4_3·a_5_3
  168. a_6_4·a_3_4 + a_4_4·a_5_5 + a_4_4·a_5_3 − a_4_3·a_5_3
  169. a_6_5·a_3_3 − a_4_4·a_5_5 + a_4_4·a_5_3
  170. a_6_5·a_3_2 + a_4_4·a_5_3 + a_4_3·a_5_3
  171. a_6_5·a_3_1 − a_4_4·a_5_3
  172. a_6_5·a_3_4 − a_4_4·a_5_5 + a_4_4·a_5_3 + a_4_3·a_5_5
  173. a_6_6·a_3_3 − a_4_4·a_5_3 − a_4_3·a_5_5 + a_4_3·a_5_3
  174. a_6_6·a_3_2 − a_4_4·a_5_3 + a_4_3·a_5_3
  175. a_6_6·a_3_1 − a_4_3·a_5_3
  176. a_6_6·a_3_4 − a_4_4·a_5_5 + a_4_4·a_5_3 − a_4_3·a_5_5 + a_4_3·a_5_3
  177. b_6_7·a_3_3 − b_4_5·a_5_2 + a_4_4·a_5_3 + a_4_3·a_5_5 − a_4_3·a_5_3
  178. b_6_7·a_3_2 + a_4_4·a_5_3 − a_4_3·a_5_3
  179. b_6_7·a_3_1 + a_4_3·a_5_3
  180. b_6_7·a_3_4 − b_4_5·a_5_2 + a_4_4·a_5_5 + a_4_4·a_5_3 + a_4_3·a_5_5 + a_4_3·a_5_3
  181.  − a_4_3·a_5_5 − a_4_3·a_5_3 + a_2_2·a_7_8
  182.  − a_4_4·a_5_5 + a_4_3·a_5_5 − a_4_3·a_5_3 + a_2_0·a_7_8
  183. a_4_4·a_5_5 − a_4_3·a_5_3 + a_2_1·a_7_8
  184. a_4_4·a_5_3 − a_4_3·a_5_5 − a_4_3·a_5_3 + a_2_2·a_7_9
  185.  − a_4_4·a_5_5 − a_4_4·a_5_3 + a_4_3·a_5_5 + a_2_0·a_7_9
  186. a_4_4·a_5_5 + a_4_3·a_5_3 + a_2_1·a_7_9
  187. a_4_4·a_5_5 − a_4_4·a_5_3 − a_4_3·a_5_5 + a_4_3·a_5_3 + a_2_2·a_7_10
  188.  − a_4_4·a_5_5 + a_4_3·a_5_5 − a_4_3·a_5_3 + a_2_0·a_7_10
  189. a_4_4·a_5_3 − a_4_3·a_5_3 + a_2_1·a_7_10
  190. a_4_4·a_5_5 − a_4_3·a_5_3 + a_2_2·a_7_11
  191. a_4_4·a_5_5 + a_4_3·a_5_5 + a_2_0·a_7_11
  192. a_4_4·a_5_5 − a_4_4·a_5_3 − a_4_3·a_5_5 − a_4_3·a_5_3 + a_2_1·a_7_11
  193. a_8_11·a_1_1 + a_4_4·a_5_3 − a_4_3·a_5_5 + a_4_3·a_5_3
  194. a_8_11·a_1_0 − a_4_4·a_5_5 − a_4_3·a_5_5 − a_4_3·a_5_3
  195. a_5_2·a_5_3
  196. a_5_3·a_5_4
  197. a_5_2·a_5_4
  198.  − a_5_4·a_5_5 − a_5_3·a_5_6 + a_5_3·a_5_5 + a_5_2·a_5_6 − a_5_2·a_5_5
  199. a_5_4·a_5_6 − a_5_4·a_5_5 − a_5_3·a_5_5 + a_5_2·a_5_5
  200.  − a_5_4·a_5_5 + a_2_1·a_2_2·c_6_8 + a_2_0·a_2_2·c_6_9 + a_2_0·a_2_2·c_6_8
  201.  − a_5_4·a_5_5 − a_5_3·a_5_5 + a_5_2·a_5_5 + a_2_1·a_2_2·c_6_9 + a_2_0·a_2_2·c_6_8
  202. a_4_3·a_6_3
  203. a_4_4·a_6_3
  204. b_4_5·a_6_3
  205. a_4_2·a_6_3
  206. a_4_3·a_6_4
  207. a_4_4·a_6_4
  208. b_4_5·a_6_4 − a_5_2·a_5_5
  209. a_4_2·a_6_4
  210. a_4_3·a_6_5
  211. a_4_4·a_6_5
  212. b_4_5·a_6_5 − a_5_2·a_5_5
  213. a_4_2·a_6_5
  214. a_4_3·a_6_6
  215. a_4_4·a_6_6
  216. b_4_5·a_6_6 − a_5_4·a_5_5 − a_5_3·a_5_6 + a_5_3·a_5_5 + a_5_2·a_5_5
  217. a_4_2·a_6_6
  218. a_4_3·b_6_7
  219. a_4_4·b_6_7
  220. a_4_2·b_6_7
  221. a_5_3·a_5_5 − a_5_2·a_5_5 + a_3_3·a_7_8
  222.  − a_5_4·a_5_5 + a_3_2·a_7_8 − a_2_1·a_2_2·c_6_8 + a_2_0·a_2_2·c_6_8
  223.  − a_5_4·a_5_5 − a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_1·a_7_8 − a_2_1·a_2_2·c_6_8
       − a_2_0·a_2_2·c_6_8
  224. a_5_4·a_5_5 − a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_4·a_7_8
  225. a_5_4·a_5_5 + a_3_3·a_7_9
  226.  − a_5_4·a_5_5 + a_3_2·a_7_9 − a_2_1·a_2_2·c_6_8 + a_2_0·a_2_2·c_6_8
  227.  − a_5_4·a_5_5 − a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_1·a_7_9 − a_2_1·a_2_2·c_6_8
       − a_2_0·a_2_2·c_6_8
  228.  − a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_4·a_7_9
  229. a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_3·a_7_10
  230.  − a_5_4·a_5_5 + a_3_2·a_7_10 + a_2_1·a_2_2·c_6_8 + a_2_0·a_2_2·c_6_8
  231.  − a_5_4·a_5_5 − a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_1·a_7_10 + a_2_0·a_2_2·c_6_8
  232. a_5_4·a_5_5 − a_5_3·a_5_5 + a_3_4·a_7_10 − a_2_1·a_2_2·c_6_8 + a_2_0·a_2_2·c_6_8
  233.  − a_5_3·a_5_6 + a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_3·a_7_11
  234. a_5_3·a_5_5 − a_5_2·a_5_5 + a_3_2·a_7_11 + a_2_1·a_2_2·c_6_8 − a_2_0·a_2_2·c_6_8
  235.  − a_5_4·a_5_5 + a_5_3·a_5_5 − a_5_2·a_5_5 + a_3_1·a_7_11 + a_2_1·a_2_2·c_6_8
       + a_2_0·a_2_2·c_6_8
  236.  − a_5_4·a_5_5 − a_5_3·a_5_6 + a_5_3·a_5_5 + a_5_2·a_5_5 + a_3_4·a_7_11 + a_2_1·a_2_2·c_6_8
       − a_2_0·a_2_2·c_6_8
  237. a_2_2·a_8_11 + a_2_0·a_2_2·c_6_8
  238. a_5_4·a_5_5 + a_2_0·a_8_11 − a_2_1·a_2_2·c_6_8 + a_2_0·a_2_2·c_6_8
  239. a_5_4·a_5_5 + a_5_3·a_5_5 − a_5_2·a_5_5 + a_2_1·a_8_11 − a_2_1·a_2_2·c_6_8
       − a_2_0·a_2_2·c_6_8
  240. a_6_3·a_5_3
  241. a_6_3·a_5_2
  242. a_6_3·a_5_5 + a_2_0·c_6_9·a_3_4 − a_2_0·c_6_9·a_3_3 − a_2_0·c_6_8·a_3_4
  243. a_6_3·a_5_4
  244. a_6_3·a_5_6 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 + a_2_0·c_6_8·a_3_4
       − a_2_0·c_6_8·a_3_3
  245. a_6_4·a_5_3
  246. a_6_4·a_5_2
  247. a_6_4·a_5_5 − a_2_0·c_6_9·a_3_4 − a_2_0·c_6_8·a_3_3
  248. a_6_4·a_5_4
  249. a_6_5·a_5_3
  250. a_6_5·a_5_2
  251. a_6_5·a_5_5 − a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 + a_2_0·c_6_8·a_3_4
  252. a_6_5·a_5_4
  253. a_6_5·a_5_6 − a_6_4·a_5_6 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_8·a_3_3
  254. a_6_6·a_5_3
  255. a_6_6·a_5_2
  256. a_6_6·a_5_5 + a_6_4·a_5_6 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 + a_2_0·c_6_8·a_3_4
       − a_2_0·c_6_8·a_3_3
  257. a_6_6·a_5_4
  258. a_6_6·a_5_6 − a_6_4·a_5_6 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 + a_2_0·c_6_8·a_3_4
       − a_2_0·c_6_8·a_3_3
  259. b_6_7·a_5_3 + b_4_52·a_3_3
  260. b_6_7·a_5_2 + b_4_52·a_3_3
  261. b_6_7·a_5_4
  262. a_4_3·a_7_8 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 − a_2_0·c_6_8·a_3_3
  263. a_4_4·a_7_8 − a_2_0·c_6_9·a_3_4 − a_2_0·c_6_8·a_3_4 + a_2_0·c_6_8·a_3_3
  264. b_4_5·a_7_8 + b_4_52·a_3_3 − a_2_0·c_6_9·a_3_4 − a_2_0·c_6_9·a_3_3 − a_2_0·c_6_8·a_3_4
       + a_2_0·c_6_8·a_3_3
  265. a_4_2·a_7_8 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_8·a_3_4 − a_2_0·c_6_8·a_3_3
  266. a_4_3·a_7_9 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 − a_2_0·c_6_8·a_3_3
  267. a_4_4·a_7_9 − a_2_0·c_6_9·a_3_4 − a_2_0·c_6_8·a_3_4 + a_2_0·c_6_8·a_3_3
  268. b_4_5·a_7_9 − b_4_52·a_3_3 − a_6_4·a_5_6 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_8·a_3_3
  269. a_4_2·a_7_9 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_8·a_3_4 − a_2_0·c_6_8·a_3_3
  270. a_4_3·a_7_10 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3
  271. a_4_4·a_7_10 − a_2_0·c_6_9·a_3_4
  272.  − b_6_7·a_5_5 + b_4_5·a_7_10 + b_4_52·a_3_3 − a_6_4·a_5_6 + a_2_0·c_6_9·a_3_4
       − a_2_0·c_6_9·a_3_3 − a_2_0·c_6_8·a_3_3
  273. a_4_2·a_7_10 + a_2_0·c_6_9·a_3_4
  274. a_4_3·a_7_11 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_8·a_3_4 + a_2_0·c_6_8·a_3_3
  275. a_4_4·a_7_11 + a_2_0·c_6_9·a_3_4 + a_2_0·c_6_9·a_3_3 − a_2_0·c_6_8·a_3_4
  276.  − b_6_7·a_5_6 − b_6_7·a_5_5 + b_4_5·a_7_11 + b_4_52·a_3_3 − a_2_0·c_6_9·a_3_3
       + a_2_0·c_6_8·a_3_4
  277. a_4_2·a_7_11 − a_2_0·c_6_9·a_3_4 − a_2_0·c_6_9·a_3_3 + a_2_0·c_6_8·a_3_4
  278. a_8_11·a_3_3 + a_6_4·a_5_6 − a_2_0·c_6_9·a_3_4 + a_2_0·c_6_8·a_3_4
  279. a_8_11·a_3_2
  280. a_8_11·a_3_1
  281. a_8_11·a_3_4 + a_6_4·a_5_6 + a_2_0·c_6_9·a_3_4 − a_2_0·c_6_8·a_3_3
  282. a_6_32
  283. a_6_42
  284. a_6_3·a_6_4
  285. a_6_4·a_6_5
  286. a_6_52
  287. a_6_3·a_6_5
  288. a_6_62
  289. a_6_4·a_6_6
  290. a_6_5·a_6_6
  291. a_6_3·a_6_6
  292. b_6_72 + b_4_53 − b_4_5·a_3_3·a_5_6 + b_4_5·a_3_3·a_5_5
  293. a_6_6·b_6_7 + b_4_5·a_3_3·a_5_6 + b_4_5·a_3_3·a_5_5
  294. a_6_4·b_6_7 + b_4_5·a_3_3·a_5_5
  295. a_6_5·b_6_7 + b_4_5·a_3_3·a_5_5
  296. a_6_3·b_6_7
  297. a_5_3·a_7_8 − a_2_2·a_4_3·c_6_9 − a_2_2·a_4_3·c_6_8 − a_2_2·a_4_2·c_6_9
  298. a_5_2·a_7_8
  299. a_5_5·a_7_8 − b_4_5·a_3_3·a_5_5 − c_6_9·a_1_0·a_5_6 − c_6_8·a_1_0·a_5_6
       − a_2_2·a_4_2·c_6_9 − a_2_2·a_4_2·c_6_8
  300. a_5_4·a_7_8 + a_2_2·a_4_3·c_6_9 − a_2_2·a_4_2·c_6_9 − a_2_2·a_4_2·c_6_8
  301. a_5_6·a_7_8 − b_4_5·a_3_3·a_5_6 + c_6_9·a_1_0·a_5_6 − c_6_8·a_1_0·a_5_6
       − a_2_2·a_4_2·c_6_9
  302. a_5_3·a_7_9 − a_2_2·a_4_3·c_6_9 − a_2_2·a_4_3·c_6_8 − a_2_2·a_4_2·c_6_9
  303. a_5_2·a_7_9
  304. a_5_5·a_7_9 + b_4_5·a_3_3·a_5_5 − c_6_9·a_1_0·a_5_6 − c_6_8·a_1_0·a_5_6
       − a_2_2·a_4_3·c_6_9 − a_2_2·a_4_3·c_6_8 − a_2_2·a_4_2·c_6_8
  305. a_5_4·a_7_9 + a_2_2·a_4_3·c_6_9 − a_2_2·a_4_2·c_6_9 − a_2_2·a_4_2·c_6_8
  306. a_5_6·a_7_9 + b_4_5·a_3_3·a_5_6 + c_6_9·a_1_0·a_5_6 − c_6_8·a_1_0·a_5_6
       − a_2_2·a_4_3·c_6_8 + a_2_2·a_4_2·c_6_9 + a_2_2·a_4_2·c_6_8
  307. a_5_3·a_7_10 + b_4_5·a_3_3·a_5_5 − a_2_2·a_4_3·c_6_9 − a_2_2·a_4_2·c_6_9
  308. a_5_2·a_7_10 + b_4_5·a_3_3·a_5_5
  309. a_5_5·a_7_10 − b_4_5·a_3_3·a_5_5 − c_6_9·a_1_0·a_5_6 − a_2_2·a_4_3·c_6_8
       − a_2_2·a_4_2·c_6_9 − a_2_2·a_4_2·c_6_8
  310. a_5_4·a_7_10 + a_2_2·a_4_3·c_6_9 − a_2_2·a_4_2·c_6_9
  311. a_5_3·a_7_11 + b_4_5·a_3_3·a_5_6 + b_4_5·a_3_3·a_5_5 + a_2_2·a_4_3·c_6_9
       − a_2_2·a_4_3·c_6_8 − a_2_2·a_4_2·c_6_9 − a_2_2·a_4_2·c_6_8
  312. a_5_2·a_7_11 + b_4_5·a_3_3·a_5_6 + b_4_5·a_3_3·a_5_5
  313. a_5_6·a_7_10 + a_5_5·a_7_11 − b_4_5·a_3_3·a_5_6 − b_4_5·a_3_3·a_5_5 − c_6_9·a_1_0·a_5_6
       − c_6_8·a_1_0·a_5_6 + a_2_2·a_4_3·c_6_8 − a_2_2·a_4_2·c_6_9 + a_2_2·a_4_2·c_6_8
  314. a_5_4·a_7_11 + a_2_2·a_4_3·c_6_9 + a_2_2·a_4_3·c_6_8 + a_2_2·a_4_2·c_6_9
       − a_2_2·a_4_2·c_6_8
  315. a_5_6·a_7_11 − a_5_6·a_7_10 − c_6_9·a_1_0·a_5_6 + c_6_8·a_1_0·a_5_6 − a_2_2·a_4_3·c_6_9
       + a_2_2·a_4_3·c_6_8 − a_2_2·a_4_2·c_6_9 + a_2_2·a_4_2·c_6_8
  316. a_4_3·a_8_11 + a_2_2·a_4_3·c_6_9 − a_2_2·a_4_3·c_6_8
  317. a_4_4·a_8_11 − a_2_2·a_4_2·c_6_9 + a_2_2·a_4_2·c_6_8
  318. b_4_5·a_8_11 − a_5_6·a_7_10 − b_4_5·a_3_3·a_5_6 + b_4_5·a_3_3·a_5_5 + c_6_9·a_1_0·a_5_6
       + c_6_8·a_1_0·a_5_6 − a_2_2·a_4_3·c_6_9 + a_2_2·a_4_2·c_6_8
  319. a_4_2·a_8_11 + a_2_2·a_4_2·c_6_9 − a_2_2·a_4_2·c_6_8
  320. b_6_7·a_7_8 + b_4_52·a_5_2 − a_2_0·c_6_9·a_5_6 − a_2_0·c_6_9·a_5_5 + a_2_0·c_6_8·a_5_5
  321. a_6_6·a_7_8 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_5 − a_2_0·c_6_9·a_5_4
       − a_2_0·c_6_8·a_5_5 + a_2_0·c_6_8·a_5_4
  322. a_6_4·a_7_8 + a_2_0·c_6_9·a_5_5 − a_2_0·c_6_8·a_5_6 + a_2_0·c_6_8·a_5_4
  323. a_6_5·a_7_8 − a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_6
       + a_2_0·c_6_8·a_5_5 + a_2_0·c_6_8·a_5_4
  324. a_6_3·a_7_8 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_6
       − a_2_0·c_6_8·a_5_5 + a_2_0·c_6_8·a_5_4
  325. b_6_7·a_7_9 − b_4_52·a_5_2 + a_3_3·a_5_5·a_5_6 − a_2_0·c_6_9·a_5_6 − a_2_0·c_6_9·a_5_5
       + a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_5
  326. a_6_6·a_7_9 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_5 + a_2_0·c_6_9·a_5_4
       − a_2_0·c_6_8·a_5_5 + a_2_0·c_6_8·a_5_4
  327. a_6_4·a_7_9 + a_2_0·c_6_9·a_5_5 + a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_6
  328. a_6_5·a_7_9 − a_2_0·c_6_9·a_5_6 − a_2_0·c_6_8·a_5_6 + a_2_0·c_6_8·a_5_5
  329. a_6_3·a_7_9 + a_2_0·c_6_9·a_5_6 − a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_6
       − a_2_0·c_6_8·a_5_5 − a_2_0·c_6_8·a_5_4
  330. b_6_7·a_7_10 + b_4_52·a_5_5 + b_4_52·a_5_2 − a_3_3·a_5_5·a_5_6 − a_2_0·c_6_9·a_5_6
       − a_2_0·c_6_9·a_5_5 − a_2_0·c_6_8·a_5_4
  331. a_6_6·a_7_10 − a_3_3·a_5_5·a_5_6 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_5
       − a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_4
  332. a_6_4·a_7_10 + a_2_0·c_6_9·a_5_5
  333. a_6_5·a_7_10 − a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_4
  334. a_6_3·a_7_10 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_4
  335. b_6_7·a_7_11 + b_4_52·a_5_6 + b_4_52·a_5_5 + b_4_52·a_5_2 − a_3_3·a_5_5·a_5_6
       − a_2_0·c_6_9·a_5_6 − a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_6 − a_2_0·c_6_8·a_5_5
       − a_2_0·c_6_8·a_5_4
  336. a_6_6·a_7_11 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_6
       + a_2_0·c_6_8·a_5_5
  337. a_6_4·a_7_11 + a_3_3·a_5_5·a_5_6 − a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_5
       − a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_5 + a_2_0·c_6_8·a_5_4
  338. a_6_5·a_7_11 + a_3_3·a_5_5·a_5_6 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_5
       − a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_6 + a_2_0·c_6_8·a_5_4
  339. a_6_3·a_7_11 − a_2_0·c_6_9·a_5_6 − a_2_0·c_6_9·a_5_5 − a_2_0·c_6_9·a_5_4
       + a_2_0·c_6_8·a_5_6 + a_2_0·c_6_8·a_5_4
  340. a_8_11·a_5_3 − a_3_3·a_5_5·a_5_6 + a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_4
  341. a_8_11·a_5_2 − a_3_3·a_5_5·a_5_6 − a_2_0·c_6_9·a_5_4 + a_2_0·c_6_8·a_5_4
  342. a_8_11·a_5_5 − a_3_3·a_5_5·a_5_6 + a_2_0·c_6_9·a_5_6 + a_2_0·c_6_9·a_5_5
       − a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_6 + a_2_0·c_6_8·a_5_4
  343. a_8_11·a_5_4 − a_2_0·c_6_9·a_5_4 − a_2_0·c_6_8·a_5_4
  344. a_8_11·a_5_6 + a_3_3·a_5_5·a_5_6 + a_2_0·c_6_9·a_5_5 + a_2_0·c_6_8·a_5_6
       − a_2_0·c_6_8·a_5_5
  345. a_7_8·a_7_9 + a_2_2·a_6_4·c_6_9 − a_2_2·a_6_4·c_6_8 + a_2_2·a_6_3·c_6_9
       − a_2_0·a_6_3·c_6_9
  346. a_7_9·a_7_10 − b_4_5·a_3_3·a_7_10 − a_2_2·a_6_4·c_6_9 + a_2_2·a_6_4·c_6_8
       − a_2_2·a_6_3·c_6_9 + a_2_2·a_6_3·c_6_8 + a_2_0·a_6_3·c_6_8
  347. a_7_8·a_7_10 + b_4_5·a_3_3·a_7_10 + a_2_2·a_6_4·c_6_8 + a_2_2·a_6_3·c_6_8
       − a_2_0·a_6_3·c_6_9 + a_2_0·a_6_3·c_6_8
  348. a_7_10·a_7_11 + b_4_5·a_5_5·a_5_6 + b_4_5·a_3_3·a_7_11 − b_4_5·a_3_3·a_7_10
       − a_2_2·a_6_4·c_6_8 + a_2_2·a_6_3·c_6_8 − a_2_0·a_6_3·c_6_9
  349. a_7_10·a_7_11 + a_7_9·a_7_11 + b_4_5·a_5_5·a_5_6 − b_4_5·a_3_3·a_7_10
       − a_2_2·a_6_3·c_6_9 − a_2_2·a_6_3·c_6_8
  350.  − a_7_10·a_7_11 + a_7_8·a_7_11 − b_4_5·a_5_5·a_5_6 + b_4_5·a_3_3·a_7_10
       + a_2_2·a_6_3·c_6_8 + a_2_0·a_6_3·c_6_9 − a_2_0·a_6_3·c_6_8
  351. b_6_7·a_8_11 − a_7_10·a_7_11 + b_4_5·a_5_5·a_5_6 + b_4_5·a_3_3·a_7_10
       − a_2_2·a_6_4·c_6_9 − a_2_2·a_6_4·c_6_8 − a_2_2·a_6_3·c_6_9 − a_2_0·a_6_3·c_6_9
       − a_2_0·a_6_3·c_6_8
  352. a_6_6·a_8_11 + a_2_2·a_6_4·c_6_9 − a_2_2·a_6_4·c_6_8 + a_2_2·a_6_3·c_6_9
       − a_2_2·a_6_3·c_6_8 + a_2_0·a_6_3·c_6_9 − a_2_0·a_6_3·c_6_8
  353. a_6_4·a_8_11 + a_2_2·a_6_4·c_6_9 − a_2_2·a_6_4·c_6_8 − a_2_0·a_6_3·c_6_8
  354. a_6_5·a_8_11 − a_2_2·a_6_3·c_6_9 + a_2_2·a_6_3·c_6_8 − a_2_0·a_6_3·c_6_9
  355. a_6_3·a_8_11 + a_2_2·a_6_3·c_6_9 − a_2_2·a_6_3·c_6_8 + a_2_0·a_6_3·c_6_9
  356. a_8_11·a_7_11 − a_3_3·a_5_5·a_7_11 + a_2_0·c_6_9·a_7_9 + a_2_0·c_6_9·a_7_8
       − a_2_0·c_6_8·a_7_9 − a_2_0·c_6_8·a_7_8 − a_2_0·c_6_92·a_1_0 − a_2_0·c_6_8·c_6_9·a_1_0
  357. a_8_11·a_7_10 + a_3_3·a_5_5·a_7_11 − a_2_0·c_6_9·a_7_9 + a_2_0·c_6_9·a_7_8
       − a_2_0·c_6_8·a_7_9 − a_2_0·c_6_8·a_7_8 − a_2_0·c_6_92·a_1_0 + a_2_0·c_6_8·c_6_9·a_1_0
  358. a_8_11·a_7_9 + a_3_3·a_5_5·a_7_11 − a_2_0·c_6_8·a_7_9 + a_2_0·c_6_8·a_7_8
       − a_2_0·c_6_92·a_1_0 + a_2_0·c_6_8·c_6_9·a_1_0 − a_2_0·c_6_82·a_1_0
  359. a_8_11·a_7_8 − a_3_3·a_5_5·a_7_11 + a_2_0·c_6_9·a_7_8 + a_2_0·c_6_8·a_7_9
       + a_2_0·c_6_8·a_7_8 − a_2_0·c_6_82·a_1_0
  360. a_8_112 + a_2_1·a_2_2·c_6_92 + a_2_1·a_2_2·c_6_8·c_6_9 + a_2_1·a_2_2·c_6_82
       + a_2_0·a_2_2·c_6_92 − a_2_0·a_2_2·c_6_8·c_6_9

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243

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_6_8, a Duflot regular element of degree 6
    2. c_6_9, a Duflot regular element of degree 6
    3. b_4_5, an element of degree 4
  • The Raw Filter Degree Type of that HSOP is [-1, -1, 9, 13].
  • 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 243

Restriction maps

Restriction map to the greatest central el. ab. subgp., which is of rank 2

  1. a_1_0 → 0, an element of degree 1
  2. a_1_1 → 0, an element of degree 1
  3. a_2_0 → 0, an element of degree 2
  4. a_2_1 → 0, an element of degree 2
  5. a_2_2 → 0, an element of degree 2
  6. a_3_1 → 0, an element of degree 3
  7. a_3_2 → 0, an element of degree 3
  8. a_3_3 → 0, an element of degree 3
  9. a_3_4 → 0, an element of degree 3
  10. a_4_2 → 0, an element of degree 4
  11. a_4_3 → 0, an element of degree 4
  12. a_4_4 → 0, an element of degree 4
  13. b_4_5 → 0, an element of degree 4
  14. a_5_2 → 0, an element of degree 5
  15. a_5_3 → 0, an element of degree 5
  16. a_5_4 → 0, an element of degree 5
  17. a_5_5 → 0, an element of degree 5
  18. a_5_6 → 0, an element of degree 5
  19. a_6_3 → 0, an element of degree 6
  20. a_6_4 → 0, an element of degree 6
  21. a_6_5 → 0, an element of degree 6
  22. a_6_6 → 0, an element of degree 6
  23. b_6_7 → 0, an element of degree 6
  24. c_6_8 → c_2_23, an element of degree 6
  25. c_6_9 → c_2_23 − c_2_13, an element of degree 6
  26. a_7_8 → 0, an element of degree 7
  27. a_7_9 → 0, an element of degree 7
  28. a_7_10 → 0, an element of degree 7
  29. a_7_11 → 0, an element of degree 7
  30. a_8_11 → 0, 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. a_1_1 → 0, an element of degree 1
  3. a_2_0 → 0, an element of degree 2
  4. a_2_1 → 0, an element of degree 2
  5. a_2_2 → 0, an element of degree 2
  6. a_3_1 → 0, an element of degree 3
  7. a_3_2 → 0, an element of degree 3
  8. a_3_3 →  − c_2_5·a_1_2, an element of degree 3
  9. a_3_4 →  − c_2_5·a_1_2, an element of degree 3
  10. a_4_2 → 0, an element of degree 4
  11. a_4_3 → 0, an element of degree 4
  12. a_4_4 → 0, an element of degree 4
  13. b_4_5 →  − c_2_52, an element of degree 4
  14. a_5_2 → c_2_52·a_1_2, an element of degree 5
  15. a_5_3 → c_2_52·a_1_2, an element of degree 5
  16. a_5_4 → 0, an element of degree 5
  17. a_5_5 →  − c_2_52·a_1_1 + c_2_4·c_2_5·a_1_2, an element of degree 5
  18. a_5_6 →  − c_2_52·a_1_2 − c_2_52·a_1_1 − c_2_52·a_1_0 + c_2_4·c_2_5·a_1_2 + c_2_3·c_2_5·a_1_2, an element of degree 5
  19. a_6_3 → 0, an element of degree 6
  20. a_6_4 →  − c_2_52·a_1_1·a_1_2, an element of degree 6
  21. a_6_5 →  − c_2_52·a_1_1·a_1_2, an element of degree 6
  22. a_6_6 → c_2_52·a_1_1·a_1_2 − c_2_52·a_1_0·a_1_2, an element of degree 6
  23. b_6_7 →  − c_2_52·a_1_0·a_1_2 + c_2_53, an element of degree 6
  24. c_6_8 → c_2_52·a_1_1·a_1_2 − c_2_52·a_1_0·a_1_2 − c_2_4·c_2_52 + c_2_43, an element of degree 6
  25. c_6_9 → c_2_52·a_1_1·a_1_2 + c_2_53 − c_2_4·c_2_52 + c_2_43 + c_2_3·c_2_52 − c_2_33, an element of degree 6
  26. a_7_8 →  − c_2_53·a_1_2, an element of degree 7
  27. a_7_9 →  − c_2_52·a_1_0·a_1_1·a_1_2 + c_2_53·a_1_2, an element of degree 7
  28. a_7_10 →  − c_2_53·a_1_2 + c_2_53·a_1_1 − c_2_4·c_2_52·a_1_2, an element of degree 7
  29. a_7_11 →  − c_2_52·a_1_0·a_1_1·a_1_2 − c_2_53·a_1_1 + c_2_53·a_1_0 + c_2_4·c_2_52·a_1_2
       − c_2_3·c_2_52·a_1_2, an element of degree 7
  30. a_8_11 → c_2_53·a_1_1·a_1_2 + c_2_53·a_1_0·a_1_2 + c_2_53·a_1_0·a_1_1
       − c_2_4·c_2_52·a_1_0·a_1_2 + c_2_3·c_2_52·a_1_1·a_1_2, an element of degree 8

About the group Ring generators Ring relations Completion information Restriction maps Back to groups of order 243


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