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Mod-5-Cohomology of HigmanSims, a group of order 44352000
General information on the group
- HigmanSims is a group of order 44352000.
- The group order factors as 29 · 32 · 53 · 7 · 11.
- The group is defined by Group([(1,60)(2,72)(3,81)(4,43)(5,11)(6,87)(7,34)(9,63)(12,46)(13,28)(14,71)(15,42)(16,97)(18,57)(19,52)(21,32)(23,47)(24,54)(25,83)(26,78)(29,89)(30,39)(33,61)(35,56)(37,67)(44,76)(45,88)(48,59)(49,86)(50,74)(51,66)(53,99)(55,75)(62,73)(65,79)(68,82)(77,92)(84,90)(85,98)(94,100),(1,86,13,10,47)(2,53,30,8,38)(3,40,48,25,17)(4,29,92,88,43)(5,98,66,54,65)(6,27,51,73,24)(7,83,16,20,28)(9,23,89,95,61)(11,42,46,91,32)(12,14,81,55,68)(15,90,31,56,37)(18,69,45,84,76)(19,59,79,35,93)(21,22,64,39,100)(26,58,96,85,77)(33,52,94,75,44)(34,62,87,78,50)(36,82,60,74,72)(41,80,70,49,67)(57,63,71,99,97)]).
- It is non-abelian.
- It has 5-Rank 2.
- The centre of a Sylow 5-subgroup has rank 1.
- Its Sylow 5-subgroup has 6 conjugacy classes of maximal elementary abelian subgroups, which are all of rank 2.
Structure of the cohomology ring
This cohomology ring is isomorphic to the cohomology ring of a subgroup, namely H*(SmallGroup(2000,474); GF(5)).
General information
- The cohomology ring is of dimension 2 and depth 1.
- The depth coincides with the Duflot bound.
- The Poincaré series is
1 − 2·t + 3·t2 − 4·t3 + 5·t4 − 5·t5 + 5·t6 − 3·t7 + 2·t8 − 2·t9 + 2·t10 − 4·t11 + 5·t12 − 4·t13 + 4·t14 − t15 − t17 + 3·t18 − 6·t19 + 7·t20 − 6·t21 + 4·t22 − t23 − t25 + 3·t26 − 4·t27 + 5·t28 − 4·t29 + 2·t30 − 2·t31 + 2·t32 − 3·t33 + 5·t34 − 5·t35 + 5·t36 − 4·t37 + 3·t38 − 2·t39 + t40 |
| ( − 1 + t)2 · (1 + t2)2 · (1 − t + t2 − t3 + t4) · (1 + t4) · (1 + t + t2 + t3 + t4) · (1 − t2 + t4 − t6 + t8) · (1 − t4 + t8 − t12 + t16) |
- The a-invariants are -∞,-16,-2. 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, -2].
Ring generators
The cohomology ring has 20 minimal generators of maximal degree 40:
- a_4_0, a nilpotent element of degree 4
- a_5_0, a nilpotent element of degree 5
- a_7_0, a nilpotent element of degree 7
- a_7_1, a nilpotent element of degree 7
- b_8_0, an element of degree 8
- b_8_1, an element of degree 8
- a_13_1, a nilpotent element of degree 13
- b_14_0, an element of degree 14
- a_15_2, a nilpotent element of degree 15
- a_16_2, a nilpotent element of degree 16
- a_18_1, a nilpotent element of degree 18
- a_19_1, a nilpotent element of degree 19
- a_23_2, a nilpotent element of degree 23
- a_24_2, a nilpotent element of degree 24
- a_27_3, a nilpotent element of degree 27
- b_28_2, an element of degree 28
- a_38_1, a nilpotent element of degree 38
- a_39_1, a nilpotent element of degree 39
- a_39_3, a nilpotent element of degree 39
- c_40_2, a Duflot element of degree 40
Ring relations
There are 10 "obvious" relations:
a_5_02, a_7_02, a_7_12, a_13_12, a_15_22, a_19_12, a_23_22, a_27_32, a_39_12, a_39_32
Apart from that, there are 164 minimal relations of maximal degree 78:
- a_4_02
- a_4_0·a_5_0
- a_4_0·a_7_0
- a_4_0·a_7_1
- a_5_0·a_7_0
- a_4_0·b_8_0
- a_4_0·b_8_1 + a_5_0·a_7_1
- b_8_0·a_5_0
- a_7_0·a_7_1
- b_8_0·a_7_1 + 2·b_8_0·a_7_0
- b_8_1·a_7_0 + b_8_0·a_7_0
- b_8_0·b_8_1 + b_8_02
- a_4_0·a_13_1
- a_4_0·b_14_0 + a_5_0·a_13_1
- a_4_0·a_15_2
- a_4_0·a_16_2
- a_5_0·a_15_2
- a_7_0·a_13_1
- a_7_1·a_13_1
- a_16_2·a_5_0
- b_8_0·a_13_1
- b_14_0·a_7_0
- b_14_0·a_7_1 − b_8_1·a_13_1
- a_4_0·a_18_1
- a_7_0·a_15_2
- a_7_1·a_15_2
- b_8_0·b_14_0
- a_4_0·a_19_1
- a_16_2·a_7_0
- a_16_2·a_7_1
- a_18_1·a_5_0
- b_8_0·a_15_2
- b_8_1·a_15_2
- a_5_0·a_19_1
- b_8_0·a_16_2
- b_8_1·a_16_2
- a_18_1·a_7_0
- a_18_1·a_7_1
- a_7_1·a_19_1 + 2·a_7_0·a_19_1
- b_8_0·a_18_1 − 2·a_7_0·a_19_1
- b_8_1·a_18_1 + 2·a_7_0·a_19_1
- a_4_0·a_23_2
- b_8_1·a_19_1 + b_8_0·a_19_1
- a_4_0·a_24_2
- a_5_0·a_23_2
- a_13_1·a_15_2
- a_16_2·a_13_1
- a_24_2·a_5_0
- b_14_0·a_15_2
- a_7_0·a_23_2
- a_7_1·a_23_2
- b_14_0·a_16_2
- a_4_0·a_27_3
- a_16_2·a_15_2
- a_18_1·a_13_1
- a_24_2·a_7_0
- a_24_2·a_7_1
- b_8_0·a_23_2
- b_8_1·a_23_2
- a_16_22
- a_5_0·a_27_3
- a_13_1·a_19_1
- a_4_0·b_28_2
- b_8_0·a_24_2
- b_8_1·a_24_2
- b_14_0·a_18_1
- a_18_1·a_15_2
- b_14_0·a_19_1
- b_28_2·a_5_0
- a_16_2·a_18_1
- a_7_0·a_27_3
- a_7_1·a_27_3
- a_15_2·a_19_1
- a_16_2·a_19_1
- b_8_1·a_27_3 + b_8_0·a_27_3
- b_28_2·a_7_0 + b_8_0·a_27_3
- b_28_2·a_7_1 − 2·b_8_0·a_27_3
- a_18_12
- a_13_1·a_23_2
- b_8_1·b_28_2 + b_8_0·b_28_2
- a_18_1·a_19_1
- a_24_2·a_13_1
- b_14_0·a_23_2
- a_15_2·a_23_2
- b_14_0·a_24_2
- a_16_2·a_23_2
- a_24_2·a_15_2
- a_16_2·a_24_2
- a_13_1·a_27_3
- a_18_1·a_23_2
- b_14_0·a_27_3
- b_28_2·a_13_1
- a_4_0·a_38_1
- a_18_1·a_24_2
- a_15_2·a_27_3
- a_19_1·a_23_2
- b_14_0·b_28_2
- a_4_0·a_39_1
- a_4_0·a_39_3
- a_16_2·a_27_3
- a_24_2·a_19_1
- a_38_1·a_5_0
- b_28_2·a_15_2
- a_5_0·a_39_1
- a_5_0·a_39_3
- a_16_2·b_28_2
- a_18_1·a_27_3
- a_38_1·a_7_0
- a_38_1·a_7_1
- a_7_0·a_39_3 − a_7_0·a_39_1
- a_7_1·a_39_1 + 2·a_7_0·a_39_1 + 2·b_14_02·a_5_0·a_13_1
- a_7_1·a_39_3 + 2·a_7_0·a_39_1
- a_19_1·a_27_3 + 2·a_7_0·a_39_1
- b_8_0·a_38_1 − 2·a_7_0·a_39_1
- b_8_1·a_38_1 + 2·a_7_0·a_39_1 + 2·b_14_02·a_5_0·a_13_1
- a_18_1·b_28_2 − a_7_0·a_39_1
- a_24_2·a_23_2
- b_8_0·a_39_3 − b_8_0·a_39_1 + b_8_05·a_7_0
- b_8_1·a_39_3 + b_8_0·a_39_1 − b_8_05·a_7_0
- b_14_03·a_5_0 + 2·b_8_1·a_39_1 + 2·b_8_0·a_39_1
- b_28_2·a_19_1 + 2·b_8_0·a_39_1 − 2·b_8_05·a_7_0
- a_24_22
- a_23_2·a_27_3
- a_24_2·a_27_3
- a_38_1·a_13_1
- b_28_2·a_23_2
- a_13_1·a_39_1 + 2·c_40_2·a_5_0·a_7_1
- a_13_1·a_39_3
- b_14_0·a_38_1 + 2·c_40_2·a_5_0·a_7_1
- a_24_2·b_28_2
- a_38_1·a_15_2
- b_14_0·a_39_1 − 2·b_8_1·c_40_2·a_5_0
- b_14_0·a_39_3
- a_16_2·a_38_1
- a_15_2·a_39_1
- a_15_2·a_39_3
- a_16_2·a_39_1
- a_16_2·a_39_3
- b_14_03·a_13_1 − b_8_1·c_40_2·a_7_1 + 2·b_8_0·c_40_2·a_7_0
- b_28_2·a_27_3 + 2·b_8_06·a_7_0 + b_8_0·c_40_2·a_7_0
- a_18_1·a_38_1
- b_14_04 − 2·b_8_13·b_14_0·a_5_0·a_13_1 − b_8_12·c_40_2 + b_8_02·c_40_2
- b_28_22 − 2·b_8_07 − b_8_02·c_40_2
- a_18_1·a_39_1
- a_18_1·a_39_3
- a_38_1·a_19_1
- a_19_1·a_39_1 + b_8_04·a_7_0·a_19_1
- a_19_1·a_39_3
- a_38_1·a_23_2
- a_24_2·a_38_1
- a_23_2·a_39_1
- a_23_2·a_39_3
- a_24_2·a_39_1
- a_24_2·a_39_3
- a_38_1·a_27_3
- a_27_3·a_39_1 − b_8_05·a_7_0·a_19_1 + 2·c_40_2·a_7_0·a_19_1
- a_27_3·a_39_3 − b_8_05·a_7_0·a_19_1 + 2·c_40_2·a_7_0·a_19_1
- b_28_2·a_38_1 + 2·b_8_05·a_7_0·a_19_1 + c_40_2·a_7_0·a_19_1
- b_28_2·a_39_1 + b_8_05·a_27_3 + b_8_06·a_19_1 − 2·b_8_0·c_40_2·a_19_1
- b_28_2·a_39_3 + b_8_06·a_19_1 − 2·b_8_0·c_40_2·a_19_1
- a_38_12
- a_38_1·a_39_1
- a_38_1·a_39_3
- a_39_1·a_39_3 − b_8_04·a_7_0·a_39_1
Data used for the Hilbert-Poincaré test
- We proved completion in degree 78 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:
- c_40_2, an element of degree 40
- b_8_1, an element of degree 8
- A Duflot regular sequence is given by c_40_2.
- The Raw Filter Degree Type of the filter regular HSOP is [-1, 24, 46].
Restriction maps
- a_4_0 → a_4_0
- a_5_0 → a_5_0
- a_7_0 → a_7_0
- a_7_1 → a_7_1
- b_8_0 → b_8_0
- b_8_1 → b_8_1
- a_13_1 → a_13_1
- b_14_0 → b_14_0
- a_15_2 → a_15_2
- a_16_2 → a_16_2
- a_18_1 → a_18_1
- a_19_1 → a_19_1
- a_23_2 → a_23_2
- a_24_2 → a_24_2
- a_27_3 → a_27_3
- b_28_2 → b_28_2
- a_38_1 → a_38_1
- a_39_1 → a_39_1
- a_39_3 → a_39_3
- c_40_2 → c_40_2
Restriction map to the greatest el. ab. subgp. in the centre of a Sylow subgroup, which is of rank 1
- a_4_0 → 0, an element of degree 4
- a_5_0 → 0, an element of degree 5
- a_7_0 → 0, an element of degree 7
- a_7_1 → 0, an element of degree 7
- b_8_0 → 0, an element of degree 8
- b_8_1 → 0, an element of degree 8
- a_13_1 → 0, an element of degree 13
- b_14_0 → 0, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → 0, an element of degree 18
- a_19_1 → 0, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → 0, an element of degree 27
- b_28_2 → 0, an element of degree 28
- a_38_1 → 0, an element of degree 38
- a_39_1 → 0, an element of degree 39
- a_39_3 → 0, an element of degree 39
- c_40_2 → c_2_020, an element of degree 40
Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup
- a_4_0 → 0, an element of degree 4
- a_5_0 → 0, an element of degree 5
- a_7_0 → c_2_23·a_1_1, an element of degree 7
- a_7_1 → − 2·c_2_23·a_1_1, an element of degree 7
- b_8_0 → 2·c_2_24, an element of degree 8
- b_8_1 → − 2·c_2_24, an element of degree 8
- a_13_1 → 0, an element of degree 13
- b_14_0 → 0, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → c_2_1·c_2_27·a_1_0·a_1_1 − c_2_15·c_2_23·a_1_0·a_1_1, an element of degree 18
- a_19_1 → − c_2_1·c_2_28·a_1_0 + c_2_12·c_2_27·a_1_1 + c_2_15·c_2_24·a_1_0
− c_2_16·c_2_23·a_1_1, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → c_2_12·c_2_211·a_1_1 − 2·c_2_16·c_2_27·a_1_1 + c_2_110·c_2_23·a_1_1, an element of degree 27
- b_28_2 → − 2·c_2_12·c_2_212 − c_2_16·c_2_28 − 2·c_2_110·c_2_24, an element of degree 28
- a_38_1 → − 2·c_2_13·c_2_215·a_1_0·a_1_1 + c_2_17·c_2_211·a_1_0·a_1_1
− c_2_111·c_2_27·a_1_0·a_1_1 + 2·c_2_115·c_2_23·a_1_0·a_1_1, an element of degree 38
- a_39_1 → c_2_219·a_1_1 + 2·c_2_13·c_2_216·a_1_0 − 2·c_2_14·c_2_215·a_1_1
− c_2_17·c_2_212·a_1_0 + c_2_18·c_2_211·a_1_1 + c_2_111·c_2_28·a_1_0 − c_2_112·c_2_27·a_1_1 − 2·c_2_115·c_2_24·a_1_0 + 2·c_2_116·c_2_23·a_1_1, an element of degree 39
- a_39_3 → 2·c_2_13·c_2_216·a_1_0 − 2·c_2_14·c_2_215·a_1_1 − c_2_17·c_2_212·a_1_0
+ c_2_18·c_2_211·a_1_1 + c_2_111·c_2_28·a_1_0 − c_2_112·c_2_27·a_1_1 − 2·c_2_115·c_2_24·a_1_0 + 2·c_2_116·c_2_23·a_1_1, an element of degree 39
- c_40_2 → c_2_220 + c_2_14·c_2_216 + c_2_18·c_2_212 + c_2_112·c_2_28
+ c_2_116·c_2_24 + c_2_120, an element of degree 40
Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup
- a_4_0 → − c_2_2·a_1_0·a_1_1, an element of degree 4
- a_5_0 → c_2_22·a_1_0 − c_2_1·c_2_2·a_1_1, an element of degree 5
- a_7_0 → 0, an element of degree 7
- a_7_1 → c_2_23·a_1_1, an element of degree 7
- b_8_0 → 0, an element of degree 8
- b_8_1 → c_2_24, an element of degree 8
- a_13_1 → − 2·c_2_1·c_2_25·a_1_1 + 2·c_2_15·c_2_2·a_1_1, an element of degree 13
- b_14_0 → − 2·c_2_1·c_2_26 + 2·c_2_15·c_2_22, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → 0, an element of degree 18
- a_19_1 → 0, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → 0, an element of degree 27
- b_28_2 → 0, an element of degree 28
- a_38_1 → c_2_13·c_2_215·a_1_0·a_1_1 + 2·c_2_17·c_2_211·a_1_0·a_1_1
− 2·c_2_111·c_2_27·a_1_0·a_1_1 − c_2_115·c_2_23·a_1_0·a_1_1, an element of degree 38
- a_39_1 → − c_2_13·c_2_216·a_1_0 + c_2_14·c_2_215·a_1_1 − 2·c_2_17·c_2_212·a_1_0
+ 2·c_2_18·c_2_211·a_1_1 + 2·c_2_111·c_2_28·a_1_0 − 2·c_2_112·c_2_27·a_1_1 + c_2_115·c_2_24·a_1_0 − c_2_116·c_2_23·a_1_1, an element of degree 39
- a_39_3 → 0, an element of degree 39
- c_40_2 → 2·c_2_12·c_2_217·a_1_0·a_1_1 + c_2_16·c_2_213·a_1_0·a_1_1
+ 2·c_2_110·c_2_29·a_1_0·a_1_1 + c_2_14·c_2_216 + c_2_18·c_2_212 + c_2_112·c_2_28 + c_2_116·c_2_24 + c_2_120, an element of degree 40
Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup
- a_4_0 → 0, an element of degree 4
- a_5_0 → 0, an element of degree 5
- a_7_0 → c_2_23·a_1_1, an element of degree 7
- a_7_1 → − 2·c_2_23·a_1_1, an element of degree 7
- b_8_0 → 2·c_2_24, an element of degree 8
- b_8_1 → − 2·c_2_24, an element of degree 8
- a_13_1 → 0, an element of degree 13
- b_14_0 → 0, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → − c_2_1·c_2_27·a_1_0·a_1_1 + c_2_15·c_2_23·a_1_0·a_1_1, an element of degree 18
- a_19_1 → c_2_1·c_2_28·a_1_0 − c_2_12·c_2_27·a_1_1 − c_2_15·c_2_24·a_1_0
+ c_2_16·c_2_23·a_1_1, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → − c_2_12·c_2_211·a_1_1 + 2·c_2_16·c_2_27·a_1_1 − c_2_110·c_2_23·a_1_1, an element of degree 27
- b_28_2 → 2·c_2_12·c_2_212 + c_2_16·c_2_28 + 2·c_2_110·c_2_24, an element of degree 28
- a_38_1 → − 2·c_2_13·c_2_215·a_1_0·a_1_1 + c_2_17·c_2_211·a_1_0·a_1_1
− c_2_111·c_2_27·a_1_0·a_1_1 + 2·c_2_115·c_2_23·a_1_0·a_1_1, an element of degree 38
- a_39_1 → c_2_219·a_1_1 + 2·c_2_13·c_2_216·a_1_0 − 2·c_2_14·c_2_215·a_1_1
− c_2_17·c_2_212·a_1_0 + c_2_18·c_2_211·a_1_1 + c_2_111·c_2_28·a_1_0 − c_2_112·c_2_27·a_1_1 − 2·c_2_115·c_2_24·a_1_0 + 2·c_2_116·c_2_23·a_1_1, an element of degree 39
- a_39_3 → 2·c_2_13·c_2_216·a_1_0 − 2·c_2_14·c_2_215·a_1_1 − c_2_17·c_2_212·a_1_0
+ c_2_18·c_2_211·a_1_1 + c_2_111·c_2_28·a_1_0 − c_2_112·c_2_27·a_1_1 − 2·c_2_115·c_2_24·a_1_0 + 2·c_2_116·c_2_23·a_1_1, an element of degree 39
- c_40_2 → c_2_220 + c_2_14·c_2_216 + c_2_18·c_2_212 + c_2_112·c_2_28
+ c_2_116·c_2_24 + c_2_120, an element of degree 40
Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup
- a_4_0 → c_2_2·a_1_0·a_1_1, an element of degree 4
- a_5_0 → − c_2_22·a_1_0 + c_2_1·c_2_2·a_1_1, an element of degree 5
- a_7_0 → 0, an element of degree 7
- a_7_1 → c_2_23·a_1_1, an element of degree 7
- b_8_0 → 0, an element of degree 8
- b_8_1 → c_2_24, an element of degree 8
- a_13_1 → 2·c_2_1·c_2_25·a_1_1 − 2·c_2_15·c_2_2·a_1_1, an element of degree 13
- b_14_0 → 2·c_2_1·c_2_26 − 2·c_2_15·c_2_22, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → 0, an element of degree 18
- a_19_1 → 0, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → 0, an element of degree 27
- b_28_2 → 0, an element of degree 28
- a_38_1 → c_2_13·c_2_215·a_1_0·a_1_1 + 2·c_2_17·c_2_211·a_1_0·a_1_1
− 2·c_2_111·c_2_27·a_1_0·a_1_1 − c_2_115·c_2_23·a_1_0·a_1_1, an element of degree 38
- a_39_1 → − c_2_13·c_2_216·a_1_0 + c_2_14·c_2_215·a_1_1 − 2·c_2_17·c_2_212·a_1_0
+ 2·c_2_18·c_2_211·a_1_1 + 2·c_2_111·c_2_28·a_1_0 − 2·c_2_112·c_2_27·a_1_1 + c_2_115·c_2_24·a_1_0 − c_2_116·c_2_23·a_1_1, an element of degree 39
- a_39_3 → 0, an element of degree 39
- c_40_2 → − 2·c_2_12·c_2_217·a_1_0·a_1_1 − c_2_16·c_2_213·a_1_0·a_1_1
− 2·c_2_110·c_2_29·a_1_0·a_1_1 + c_2_14·c_2_216 + c_2_18·c_2_212 + c_2_112·c_2_28 + c_2_116·c_2_24 + c_2_120, an element of degree 40
Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup
- a_4_0 → − 2·c_2_2·a_1_0·a_1_1, an element of degree 4
- a_5_0 → 2·c_2_22·a_1_0 − 2·c_2_1·c_2_2·a_1_1, an element of degree 5
- a_7_0 → 0, an element of degree 7
- a_7_1 → c_2_23·a_1_1, an element of degree 7
- b_8_0 → 0, an element of degree 8
- b_8_1 → c_2_24, an element of degree 8
- a_13_1 → c_2_1·c_2_25·a_1_1 − c_2_15·c_2_2·a_1_1, an element of degree 13
- b_14_0 → c_2_1·c_2_26 − c_2_15·c_2_22, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → 0, an element of degree 18
- a_19_1 → 0, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → 0, an element of degree 27
- b_28_2 → 0, an element of degree 28
- a_38_1 → c_2_13·c_2_215·a_1_0·a_1_1 + 2·c_2_17·c_2_211·a_1_0·a_1_1
− 2·c_2_111·c_2_27·a_1_0·a_1_1 − c_2_115·c_2_23·a_1_0·a_1_1, an element of degree 38
- a_39_1 → − c_2_13·c_2_216·a_1_0 + c_2_14·c_2_215·a_1_1 − 2·c_2_17·c_2_212·a_1_0
+ 2·c_2_18·c_2_211·a_1_1 + 2·c_2_111·c_2_28·a_1_0 − 2·c_2_112·c_2_27·a_1_1 + c_2_115·c_2_24·a_1_0 − c_2_116·c_2_23·a_1_1, an element of degree 39
- a_39_3 → 0, an element of degree 39
- c_40_2 → c_2_12·c_2_217·a_1_0·a_1_1 − 2·c_2_16·c_2_213·a_1_0·a_1_1
+ c_2_110·c_2_29·a_1_0·a_1_1 + c_2_14·c_2_216 + c_2_18·c_2_212 + c_2_112·c_2_28 + c_2_116·c_2_24 + c_2_120, an element of degree 40
Restriction map to a maximal el. ab. subgp. of rank 2 in a Sylow subgroup
- a_4_0 → 2·c_2_2·a_1_0·a_1_1, an element of degree 4
- a_5_0 → − 2·c_2_22·a_1_0 + 2·c_2_1·c_2_2·a_1_1, an element of degree 5
- a_7_0 → 0, an element of degree 7
- a_7_1 → c_2_23·a_1_1, an element of degree 7
- b_8_0 → 0, an element of degree 8
- b_8_1 → c_2_24, an element of degree 8
- a_13_1 → − c_2_1·c_2_25·a_1_1 + c_2_15·c_2_2·a_1_1, an element of degree 13
- b_14_0 → − c_2_1·c_2_26 + c_2_15·c_2_22, an element of degree 14
- a_15_2 → 0, an element of degree 15
- a_16_2 → 0, an element of degree 16
- a_18_1 → 0, an element of degree 18
- a_19_1 → 0, an element of degree 19
- a_23_2 → 0, an element of degree 23
- a_24_2 → 0, an element of degree 24
- a_27_3 → 0, an element of degree 27
- b_28_2 → 0, an element of degree 28
- a_38_1 → c_2_13·c_2_215·a_1_0·a_1_1 + 2·c_2_17·c_2_211·a_1_0·a_1_1
− 2·c_2_111·c_2_27·a_1_0·a_1_1 − c_2_115·c_2_23·a_1_0·a_1_1, an element of degree 38
- a_39_1 → − c_2_13·c_2_216·a_1_0 + c_2_14·c_2_215·a_1_1 − 2·c_2_17·c_2_212·a_1_0
+ 2·c_2_18·c_2_211·a_1_1 + 2·c_2_111·c_2_28·a_1_0 − 2·c_2_112·c_2_27·a_1_1 + c_2_115·c_2_24·a_1_0 − c_2_116·c_2_23·a_1_1, an element of degree 39
- a_39_3 → 0, an element of degree 39
- c_40_2 → − c_2_12·c_2_217·a_1_0·a_1_1 + 2·c_2_16·c_2_213·a_1_0·a_1_1
− c_2_110·c_2_29·a_1_0·a_1_1 + c_2_14·c_2_216 + c_2_18·c_2_212 + c_2_112·c_2_28 + c_2_116·c_2_24 + c_2_120, an element of degree 40
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