Simon King
David J. Green
Cohomology
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Singular
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Cohomology of group number 1144 of order 128
General information on the group
- The group has 4 minimal generators and exponent 4.
- It is non-abelian.
- It has p-Rank 5.
- Its center has rank 3.
- It has 2 conjugacy classes of maximal elementary abelian subgroups, which are of rank 4 and 5, respectively.
Structure of the cohomology ring
General information
- The cohomology ring is of dimension 5 and depth 3.
- The depth coincides with the Duflot bound.
- The Poincaré series is
t4 − 2·t3 + t2 − t − 1 |
| (t + 1)2 · (t − 1)5 · (t2 + 1) |
- The a-invariants are -∞,-∞,-∞,-6,-5,-5. They were obtained using the filter regular HSOP of the Benson test.
Ring generators
The cohomology ring has 12 minimal generators of maximal degree 5:
- a_1_0, a nilpotent element of degree 1
- b_1_1, an element of degree 1
- b_1_2, an element of degree 1
- b_1_3, an element of degree 1
- c_2_7, a Duflot regular element of degree 2
- c_2_8, a Duflot regular element of degree 2
- b_3_15, an element of degree 3
- b_3_16, an element of degree 3
- b_3_17, an element of degree 3
- b_3_18, an element of degree 3
- c_4_33, a Duflot regular element of degree 4
- b_5_57, an element of degree 5
Ring relations
There are 29 minimal relations of maximal degree 10:
- a_1_0·b_1_2 + a_1_02
- b_1_1·b_1_2
- b_1_2·b_1_3 + b_1_22 + a_1_0·b_1_3 + a_1_0·b_1_1
- a_1_02·b_1_3
- b_1_2·b_3_15
- a_1_0·b_3_15
- a_1_0·b_3_16
- b_1_2·b_3_17 + b_1_2·b_3_16 + c_2_8·b_1_22 + c_2_8·a_1_02
- b_1_1·b_3_16 + a_1_0·b_3_17
- b_1_3·b_3_16 + b_1_2·b_3_18 + b_1_24 + b_1_1·b_3_16 + c_2_8·b_1_22 + c_2_7·a_1_0·b_1_3
+ c_2_7·a_1_0·b_1_1 + c_2_8·a_1_02
- b_1_3·b_3_16 + b_1_2·b_3_16 + b_1_1·b_3_16 + a_1_0·b_3_18 + c_2_7·a_1_0·b_1_3
+ c_2_7·a_1_0·b_1_1 + c_2_7·a_1_02
- b_1_3·b_3_15 + b_1_1·b_3_18 + c_2_7·b_1_1·b_1_3 + c_2_7·b_1_12 + c_2_8·a_1_0·b_1_1
- b_3_152 + c_2_7·b_1_12·b_1_32 + c_2_7·b_1_14
- b_3_15·b_3_16
- b_3_16·b_3_18 + b_3_162 + b_1_23·b_3_16 + c_2_8·b_1_2·b_3_16 + c_2_7·a_1_0·b_3_18
+ c_2_7·a_1_0·b_1_33 + c_2_7·a_1_0·b_1_13 + c_2_72·a_1_0·b_1_3 + c_2_72·a_1_0·b_1_1 + c_2_72·a_1_02
- b_3_15·b_3_18 + c_2_7·b_1_1·b_3_18 + c_2_7·b_1_1·b_3_15 + c_2_7·b_1_1·b_1_33
+ c_2_7·b_1_13·b_1_3 + c_2_72·b_1_1·b_1_3 + c_2_72·b_1_12 + c_2_7·c_2_8·a_1_0·b_1_1
- b_3_182 + b_1_23·b_3_16 + a_1_0·b_1_32·b_3_18 + c_4_33·b_1_22 + c_2_8·b_1_24
+ c_2_7·b_1_34 + c_2_7·b_1_12·b_1_32 + c_2_7·a_1_0·b_1_33 + c_2_7·a_1_0·b_1_13 + c_2_82·b_1_22 + c_2_7·c_2_8·b_1_22 + c_2_72·b_1_32 + c_2_72·b_1_22 + c_2_72·b_1_12 + c_2_82·a_1_02
- b_3_16·b_3_17 + b_3_162 + c_2_8·b_1_2·b_3_16 + c_4_33·a_1_0·b_1_1
+ c_2_7·c_2_8·a_1_0·b_1_1
- b_3_172 + b_3_162 + b_1_12·b_1_3·b_3_18 + b_1_12·b_1_3·b_3_17 + b_1_13·b_3_17
+ a_1_0·b_1_12·b_3_17 + c_4_33·b_1_12 + c_2_7·b_1_12·b_1_32 + c_2_7·b_1_13·b_1_3 + c_2_8·a_1_0·b_1_13 + c_2_82·b_1_22 + c_2_7·c_2_8·b_1_12 + c_2_82·a_1_02
- b_3_182 + b_3_162 + b_1_26 + a_1_0·b_1_32·b_3_18 + c_2_7·b_1_34 + c_2_7·b_1_24
+ c_2_7·b_1_12·b_1_32 + c_2_7·a_1_0·b_1_33 + c_2_7·a_1_0·b_1_13 + c_4_33·a_1_02 + c_2_82·b_1_22 + c_2_72·b_1_32 + c_2_72·b_1_22 + c_2_72·b_1_12 + c_2_82·a_1_02 + c_2_7·c_2_8·a_1_02
- b_3_182 + b_3_17·b_3_18 + b_3_16·b_3_18 + b_3_16·b_3_17 + b_3_162 + b_1_3·b_5_57
+ b_1_33·b_3_17 + b_1_23·b_3_16 + b_1_26 + b_1_1·b_1_32·b_3_18 + b_1_12·b_1_3·b_3_18 + b_1_12·b_1_3·b_3_17 + b_1_13·b_3_18 + a_1_0·b_1_32·b_3_18 + c_4_33·b_1_32 + c_2_8·b_1_3·b_3_18 + c_2_8·b_1_24 + c_2_7·b_1_1·b_3_17 + c_2_7·b_1_12·b_1_32 + c_2_7·b_1_13·b_1_3 + c_2_7·b_1_14 + c_4_33·a_1_0·b_1_3 + c_2_8·a_1_0·b_3_17 + c_2_7·a_1_0·b_3_17 + c_2_7·a_1_0·b_1_33 + c_2_7·a_1_0·b_1_13 + c_2_82·b_1_32 + c_2_7·c_2_8·b_1_32 + c_2_72·b_1_32 + c_2_72·b_1_12 + c_2_82·a_1_0·b_1_3 + c_2_7·c_2_8·a_1_0·b_1_1 + c_2_72·a_1_0·b_1_3 + c_2_72·a_1_0·b_1_1 + c_2_7·c_2_8·a_1_02
- b_3_16·b_3_17 + b_3_162 + b_1_2·b_5_57 + b_1_23·b_3_16 + b_1_26 + c_2_8·b_1_24
+ c_2_7·b_1_24 + c_4_33·a_1_0·b_1_3 + c_2_8·a_1_0·b_3_18 + c_2_7·a_1_0·b_1_33 + c_2_7·a_1_0·b_1_13 + c_2_72·b_1_22 + c_2_82·a_1_0·b_1_3 + c_2_82·a_1_0·b_1_1 + c_2_7·c_2_8·a_1_0·b_1_3
- b_3_182 + b_3_162 + b_1_26 + a_1_0·b_5_57 + a_1_0·b_1_32·b_3_18 + c_2_7·b_1_34
+ c_2_7·b_1_24 + c_2_7·b_1_12·b_1_32 + c_4_33·a_1_0·b_1_3 + c_2_8·a_1_0·b_3_18 + c_2_7·a_1_0·b_3_17 + c_2_7·a_1_0·b_1_13 + c_2_82·b_1_22 + c_2_72·b_1_32 + c_2_72·b_1_22 + c_2_72·b_1_12 + c_2_82·a_1_0·b_1_3 + c_2_7·c_2_8·a_1_0·b_1_3 + c_2_7·c_2_8·a_1_02 + c_2_72·a_1_02
- b_3_15·b_3_17 + b_1_1·b_5_57 + b_1_1·b_1_32·b_3_17 + b_1_12·b_1_3·b_3_18
+ b_1_13·b_3_18 + b_1_13·b_3_17 + b_1_13·b_3_15 + c_4_33·b_1_1·b_1_3 + c_2_8·b_1_1·b_3_18 + c_2_7·b_1_1·b_3_17 + c_2_7·b_1_1·b_1_33 + c_2_8·a_1_0·b_1_13 + c_2_7·a_1_0·b_3_17 + c_2_82·b_1_1·b_1_3 + c_2_7·c_2_8·b_1_1·b_1_3 + c_2_82·a_1_0·b_1_1
- b_3_16·b_5_57 + b_1_28 + c_4_33·b_1_24 + c_2_7·b_1_23·b_3_16 + c_2_7·b_1_26
+ c_4_33·a_1_0·b_3_18 + c_4_33·a_1_0·b_3_17 + c_2_7·a_1_0·b_1_32·b_3_18 + c_2_7·a_1_0·b_1_12·b_3_17 + c_2_8·c_4_33·b_1_22 + c_2_82·b_1_24 + c_2_72·b_1_2·b_3_16 + c_2_82·a_1_0·b_3_18 + c_2_82·a_1_0·b_3_17 + c_2_7·c_4_33·a_1_0·b_1_3 + c_2_7·c_2_8·a_1_0·b_3_17 + c_2_7·c_2_8·a_1_0·b_1_33 + c_2_7·c_2_8·a_1_0·b_1_13 + c_2_72·a_1_0·b_1_33 + c_2_72·a_1_0·b_1_13 + c_2_8·c_4_33·a_1_02 + c_2_7·c_4_33·a_1_02 + c_2_7·c_2_82·b_1_22 + c_2_7·c_2_82·a_1_0·b_1_3 + c_2_7·c_2_82·a_1_0·b_1_1 + c_2_72·c_2_8·a_1_0·b_1_1
- b_3_18·b_5_57 + b_3_15·b_5_57 + b_1_33·b_5_57 + b_1_35·b_3_17 + b_1_25·b_3_16
+ b_1_28 + b_1_1·b_1_32·b_5_57 + b_1_1·b_1_34·b_3_18 + b_1_1·b_1_34·b_3_17 + b_1_12·b_1_3·b_5_57 + b_1_13·b_5_57 + b_1_13·b_1_32·b_3_18 + b_1_14·b_1_3·b_3_18 + b_1_14·b_1_3·b_3_17 + b_1_15·b_3_17 + b_1_15·b_3_15 + c_4_33·b_1_3·b_3_18 + c_4_33·b_1_34 + c_4_33·b_1_2·b_3_16 + c_4_33·b_1_24 + c_4_33·b_1_1·b_3_18 + c_4_33·b_1_1·b_1_33 + c_4_33·b_1_12·b_1_32 + c_4_33·b_1_13·b_1_3 + c_2_8·b_1_33·b_3_18 + c_2_8·b_1_26 + c_2_8·b_1_1·b_1_32·b_3_18 + c_2_8·b_1_12·b_1_3·b_3_18 + c_2_8·b_1_13·b_3_18 + c_2_7·b_1_33·b_3_18 + c_2_7·b_1_33·b_3_17 + c_2_7·b_1_36 + c_2_7·b_1_23·b_3_16 + c_2_7·b_1_26 + c_2_7·b_1_1·b_1_32·b_3_18 + c_2_7·b_1_1·b_1_32·b_3_17 + c_2_7·b_1_12·b_1_3·b_3_18 + c_2_7·b_1_12·b_1_3·b_3_17 + c_2_7·b_1_12·b_1_34 + c_2_7·b_1_13·b_3_18 + c_2_7·b_1_13·b_3_17 + c_2_7·b_1_13·b_1_33 + c_2_7·b_1_14·b_1_32 + c_4_33·a_1_0·b_3_18 + c_4_33·a_1_0·b_1_33 + c_4_33·a_1_0·b_1_13 + c_2_8·a_1_0·b_1_32·b_3_18 + c_2_8·a_1_0·b_1_15 + c_2_7·a_1_0·b_1_35 + c_2_7·a_1_0·b_1_15 + c_2_82·b_1_3·b_3_18 + c_2_82·b_1_34 + c_2_82·b_1_24 + c_2_82·b_1_1·b_3_18 + c_2_82·b_1_1·b_1_33 + c_2_82·b_1_12·b_1_32 + c_2_82·b_1_13·b_1_3 + c_2_7·c_4_33·b_1_1·b_1_3 + c_2_7·c_4_33·b_1_12 + c_2_7·c_2_8·b_1_3·b_3_18 + c_2_7·c_2_8·b_1_2·b_3_16 + c_2_7·c_2_8·b_1_1·b_3_15 + c_2_72·b_1_3·b_3_17 + c_2_72·b_1_1·b_3_17 + c_2_72·b_1_12·b_1_32 + c_2_72·b_1_13·b_1_3 + c_2_8·c_4_33·a_1_0·b_1_1 + c_2_82·a_1_0·b_3_18 + c_2_82·a_1_0·b_1_33 + c_2_82·a_1_0·b_1_13 + c_2_7·c_2_8·a_1_0·b_3_17 + c_2_7·c_2_8·a_1_0·b_1_33 + c_2_72·a_1_0·b_1_33 + c_2_72·a_1_0·b_1_13 + c_2_8·c_4_33·a_1_02 + c_2_7·c_4_33·a_1_02 + c_2_83·b_1_22 + c_2_7·c_2_82·b_1_1·b_1_3 + c_2_7·c_2_82·b_1_12 + c_2_72·c_2_8·b_1_32 + c_2_72·c_2_8·b_1_22 + c_2_72·c_2_8·b_1_12 + c_2_83·a_1_0·b_1_1 + c_2_73·a_1_0·b_1_3 + c_2_73·a_1_0·b_1_1 + c_2_83·a_1_02 + c_2_7·c_2_82·a_1_02
- b_3_17·b_5_57 + b_1_28 + b_1_1·b_1_32·b_5_57 + b_1_1·b_1_34·b_3_17
+ b_1_12·b_1_33·b_3_17 + b_1_13·b_1_32·b_3_18 + b_1_14·b_1_3·b_3_17 + b_1_15·b_3_17 + c_4_33·b_1_3·b_3_17 + c_4_33·b_1_2·b_3_16 + c_4_33·b_1_24 + c_4_33·b_1_1·b_3_15 + c_4_33·b_1_1·b_1_33 + c_4_33·b_1_12·b_1_32 + c_4_33·b_1_14 + c_2_8·b_1_3·b_5_57 + c_2_8·b_1_33·b_3_17 + c_2_8·b_1_23·b_3_16 + c_2_8·b_1_12·b_1_3·b_3_18 + c_2_8·b_1_12·b_1_3·b_3_17 + c_2_8·b_1_13·b_3_18 + c_2_7·b_1_33·b_3_17 + c_2_7·b_1_26 + c_2_7·b_1_1·b_1_35 + c_2_7·b_1_12·b_1_3·b_3_18 + c_2_7·b_1_12·b_1_3·b_3_17 + c_2_7·b_1_13·b_1_33 + c_2_7·b_1_14·b_1_32 + c_2_8·a_1_0·b_1_12·b_3_17 + c_2_8·c_4_33·b_1_32 + c_2_8·c_4_33·b_1_22 + c_2_82·b_1_3·b_3_18 + c_2_82·b_1_3·b_3_17 + c_2_82·b_1_24 + c_2_82·b_1_1·b_1_33 + c_2_7·c_4_33·b_1_12 + c_2_7·c_2_8·b_1_3·b_3_17 + c_2_7·c_2_8·b_1_34 + c_2_7·c_2_8·b_1_2·b_3_16 + c_2_7·c_2_8·b_1_1·b_3_17 + c_2_7·c_2_8·b_1_1·b_3_15 + c_2_7·c_2_8·b_1_1·b_1_33 + c_2_7·c_2_8·b_1_12·b_1_32 + c_2_7·c_2_8·b_1_13·b_1_3 + c_2_72·b_1_2·b_3_16 + c_2_72·b_1_12·b_1_32 + c_2_72·b_1_13·b_1_3 + c_2_8·c_4_33·a_1_0·b_1_3 + c_2_8·c_4_33·a_1_0·b_1_1 + c_2_82·a_1_0·b_1_13 + c_2_7·c_4_33·a_1_0·b_1_1 + c_2_7·c_2_8·a_1_0·b_3_18 + c_2_7·c_2_8·a_1_0·b_3_17 + c_2_7·c_2_8·a_1_0·b_1_33 + c_2_83·b_1_32 + c_2_83·b_1_22 + c_2_7·c_2_82·b_1_32 + c_2_7·c_2_82·b_1_22 + c_2_72·c_2_8·b_1_12 + c_2_83·a_1_0·b_1_3 + c_2_72·c_2_8·a_1_0·b_1_1 + c_2_83·a_1_02 + c_2_7·c_2_82·a_1_02
- b_3_18·b_5_57 + b_1_33·b_5_57 + b_1_35·b_3_17 + b_1_25·b_3_16 + b_1_28
+ b_1_1·b_1_34·b_3_18 + b_1_12·b_1_3·b_5_57 + b_1_12·b_1_33·b_3_18 + b_1_14·b_1_3·b_3_18 + b_1_14·b_1_3·b_3_17 + b_1_15·b_3_18 + c_4_33·b_1_3·b_3_18 + c_4_33·b_1_34 + c_4_33·b_1_2·b_3_16 + c_4_33·b_1_24 + c_4_33·b_1_12·b_1_32 + c_2_8·b_1_33·b_3_18 + c_2_8·b_1_26 + c_2_8·b_1_12·b_1_3·b_3_18 + c_2_7·b_1_33·b_3_18 + c_2_7·b_1_33·b_3_17 + c_2_7·b_1_36 + c_2_7·b_1_23·b_3_16 + c_2_7·b_1_26 + c_2_7·b_1_1·b_5_57 + c_2_7·b_1_1·b_1_35 + c_2_7·b_1_12·b_1_3·b_3_18 + c_2_7·b_1_12·b_1_3·b_3_17 + c_2_7·b_1_13·b_1_33 + c_2_7·b_1_16 + c_4_33·a_1_0·b_3_18 + c_4_33·a_1_0·b_1_33 + c_4_33·a_1_0·b_1_13 + c_2_8·a_1_0·b_1_32·b_3_18 + c_2_7·a_1_0·b_1_35 + c_2_7·a_1_0·b_1_15 + c_2_82·b_1_3·b_3_18 + c_2_82·b_1_34 + c_2_82·b_1_24 + c_2_82·b_1_12·b_1_32 + c_2_7·c_4_33·b_1_1·b_1_3 + c_2_7·c_2_8·b_1_3·b_3_18 + c_2_7·c_2_8·b_1_2·b_3_16 + c_2_7·c_2_8·b_1_1·b_3_18 + c_2_72·b_1_3·b_3_17 + c_2_72·b_1_12·b_1_32 + c_2_82·a_1_0·b_3_18 + c_2_82·a_1_0·b_1_33 + c_2_82·a_1_0·b_1_13 + c_2_7·c_2_8·a_1_0·b_3_17 + c_2_7·c_2_8·a_1_0·b_1_33 + c_2_7·c_2_8·a_1_0·b_1_13 + c_2_72·a_1_0·b_3_17 + c_2_72·a_1_0·b_1_33 + c_2_72·a_1_0·b_1_13 + c_2_8·c_4_33·a_1_02 + c_2_7·c_4_33·a_1_02 + c_2_83·b_1_22 + c_2_7·c_2_82·b_1_1·b_1_3 + c_2_72·c_2_8·b_1_32 + c_2_72·c_2_8·b_1_22 + c_2_72·c_2_8·b_1_1·b_1_3 + c_2_72·c_2_8·b_1_12 + c_2_7·c_2_82·a_1_0·b_1_1 + c_2_73·a_1_0·b_1_3 + c_2_73·a_1_0·b_1_1 + c_2_83·a_1_02 + c_2_7·c_2_82·a_1_02
- b_5_572 + b_1_27·b_3_16 + b_1_12·b_1_35·b_3_18 + b_1_12·b_1_35·b_3_17
+ b_1_13·b_1_34·b_3_17 + b_1_16·b_1_3·b_3_18 + b_1_16·b_1_3·b_3_17 + b_1_17·b_3_17 + c_4_33·b_1_26 + c_4_33·b_1_12·b_1_34 + c_4_33·b_1_16 + c_2_8·b_1_28 + c_2_7·b_1_28 + c_2_7·b_1_12·b_1_33·b_3_18 + c_2_7·b_1_12·b_1_33·b_3_17 + c_2_7·b_1_13·b_1_32·b_3_17 + c_2_7·b_1_13·b_1_35 + c_2_7·b_1_14·b_1_3·b_3_18 + c_2_7·b_1_14·b_1_3·b_3_17 + c_2_7·b_1_15·b_3_17 + c_2_7·b_1_16·b_1_32 + c_2_7·b_1_17·b_1_3 + c_2_7·b_1_18 + c_4_332·b_1_32 + c_4_332·b_1_22 + c_2_82·b_1_23·b_3_16 + c_2_7·c_4_33·b_1_12·b_1_32 + c_2_7·c_4_33·b_1_14 + c_2_7·c_2_8·b_1_26 + c_2_7·c_2_8·b_1_12·b_1_34 + c_2_7·c_2_8·b_1_16 + c_2_72·b_1_36 + c_2_72·b_1_12·b_1_3·b_3_18 + c_2_72·b_1_12·b_1_3·b_3_17 + c_2_72·b_1_13·b_3_17 + c_2_72·b_1_13·b_1_33 + c_2_72·b_1_14·b_1_32 + c_2_72·b_1_15·b_1_3 + c_2_72·b_1_16 + c_2_82·a_1_0·b_1_32·b_3_18 + c_2_72·a_1_0·b_1_12·b_3_17 + c_2_82·c_4_33·b_1_22 + c_2_83·b_1_24 + c_2_7·c_2_82·b_1_34 + c_2_7·c_2_82·b_1_12·b_1_32 + c_2_72·c_4_33·b_1_12 + c_2_72·c_2_8·b_1_12·b_1_32 + c_2_72·c_2_8·b_1_14 + c_2_73·b_1_12·b_1_32 + c_2_73·b_1_13·b_1_3 + c_2_7·c_2_82·a_1_0·b_1_33 + c_2_7·c_2_82·a_1_0·b_1_13 + c_2_72·c_2_8·a_1_0·b_1_13 + c_2_84·b_1_32 + c_2_84·b_1_22 + c_2_7·c_2_83·b_1_22 + c_2_72·c_2_82·b_1_12 + c_2_73·c_2_8·b_1_12 + c_2_74·b_1_22 + c_2_72·c_2_82·a_1_02
Data used for Benson′s test
- Benson′s completion test succeeded in degree 10.
- 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_2_7, a Duflot regular element of degree 2
- c_2_8, a Duflot regular element of degree 2
- c_4_33, a Duflot regular element of degree 4
- b_1_32 + b_1_1·b_1_3 + b_1_12, an element of degree 2
- b_1_32, an element of degree 2
- The Raw Filter Degree Type of that HSOP is [-1, -1, -1, 2, 5, 7].
- The filter degree type of any filter regular HSOP is [-1, -2, -3, -4, -5, -5].
Restriction maps
Restriction map to the greatest central el. ab. subgp., which is of rank 3
- a_1_0 → 0, an element of degree 1
- b_1_1 → 0, an element of degree 1
- b_1_2 → 0, an element of degree 1
- b_1_3 → 0, an element of degree 1
- c_2_7 → c_1_12, an element of degree 2
- c_2_8 → c_1_22, an element of degree 2
- b_3_15 → 0, an element of degree 3
- b_3_16 → 0, an element of degree 3
- b_3_17 → 0, an element of degree 3
- b_3_18 → 0, an element of degree 3
- c_4_33 → c_1_12·c_1_22 + c_1_04, an element of degree 4
- b_5_57 → 0, an element of degree 5
Restriction map to a maximal el. ab. subgp. of rank 4
- a_1_0 → 0, an element of degree 1
- b_1_1 → 0, an element of degree 1
- b_1_2 → c_1_3, an element of degree 1
- b_1_3 → c_1_3, an element of degree 1
- c_2_7 → c_1_1·c_1_3 + c_1_12, an element of degree 2
- c_2_8 → c_1_2·c_1_3 + c_1_22, an element of degree 2
- b_3_15 → 0, an element of degree 3
- b_3_16 → c_1_33 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
- b_3_17 → c_1_33 + c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
- b_3_18 → c_1_2·c_1_32 + c_1_22·c_1_3 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
- c_4_33 → c_1_34 + c_1_2·c_1_33 + c_1_22·c_1_32 + c_1_1·c_1_33 + c_1_1·c_1_2·c_1_32
+ c_1_1·c_1_22·c_1_3 + c_1_12·c_1_32 + c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22 + c_1_0·c_1_33 + c_1_04, an element of degree 4
- b_5_57 → c_1_1·c_1_34 + c_1_14·c_1_3 + c_1_0·c_1_34 + c_1_0·c_1_2·c_1_33
+ c_1_0·c_1_22·c_1_32 + c_1_02·c_1_33 + c_1_02·c_1_2·c_1_32 + c_1_02·c_1_22·c_1_3, an element of degree 5
Restriction map to a maximal el. ab. subgp. of rank 5
- a_1_0 → 0, an element of degree 1
- b_1_1 → c_1_3, an element of degree 1
- b_1_2 → 0, an element of degree 1
- b_1_3 → c_1_4, an element of degree 1
- c_2_7 → c_1_12, an element of degree 2
- c_2_8 → c_1_2·c_1_3 + c_1_22, an element of degree 2
- b_3_15 → c_1_1·c_1_3·c_1_4 + c_1_1·c_1_32, an element of degree 3
- b_3_16 → 0, an element of degree 3
- b_3_17 → c_1_1·c_1_3·c_1_4 + c_1_1·c_1_32 + c_1_0·c_1_3·c_1_4 + c_1_0·c_1_32 + c_1_02·c_1_3, an element of degree 3
- b_3_18 → c_1_1·c_1_42 + c_1_1·c_1_3·c_1_4 + c_1_12·c_1_4 + c_1_12·c_1_3, an element of degree 3
- c_4_33 → c_1_1·c_1_43 + c_1_1·c_1_33 + c_1_12·c_1_42 + c_1_12·c_1_32
+ c_1_12·c_1_2·c_1_3 + c_1_12·c_1_22 + c_1_0·c_1_3·c_1_42 + c_1_0·c_1_33 + c_1_02·c_1_42 + c_1_02·c_1_3·c_1_4 + c_1_04, an element of degree 4
- b_5_57 → c_1_22·c_1_32·c_1_4 + c_1_24·c_1_4 + c_1_1·c_1_44 + c_1_1·c_1_32·c_1_42
+ c_1_1·c_1_2·c_1_3·c_1_42 + c_1_1·c_1_2·c_1_32·c_1_4 + c_1_1·c_1_22·c_1_42 + c_1_1·c_1_22·c_1_3·c_1_4 + c_1_12·c_1_32·c_1_4 + c_1_12·c_1_2·c_1_3·c_1_4 + c_1_12·c_1_2·c_1_32 + c_1_12·c_1_22·c_1_4 + c_1_12·c_1_22·c_1_3 + c_1_13·c_1_3·c_1_4 + c_1_13·c_1_32 + c_1_0·c_1_32·c_1_42 + c_1_0·c_1_34 + c_1_0·c_1_1·c_1_3·c_1_42 + c_1_0·c_1_1·c_1_33 + c_1_0·c_1_12·c_1_3·c_1_4 + c_1_0·c_1_12·c_1_32 + c_1_02·c_1_43 + c_1_02·c_1_33 + c_1_02·c_1_1·c_1_3·c_1_4 + c_1_02·c_1_1·c_1_32 + c_1_02·c_1_12·c_1_3 + c_1_04·c_1_4, an element of degree 5
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