# Difference between revisions of "ApCoCoA-1:Other1 groups"

From ApCoCoAWiki

(New page: === <div id="Higman_groups">Higman group</div> === ==== Description ==== This group has the following representation: G = <a,b | a^{2}b^{-6} = (ab...) |
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− | === <div id=" | + | === <div id="Other_groups">[[:ApCoCoA:Symbolic data#Other_groups|Other groups]]</div> === |

==== Description ==== | ==== Description ==== | ||

This group has the following representation: | This group has the following representation: |

## Revision as of 11:38, 18 September 2013

#### Description

This group has the following representation:

G = <a,b | a^{2}b^{-6} = (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1>

where k is congruent to 3 mod 6.

#### Reference

No reference available

#### Computation

/*Use the ApCoCoA package ncpoly.*/ // a is invers to c and b is invers to d Use ZZ/(2)[a,b,c,d]; NC.SetOrdering("LLEX"); Define CreateRelationsOther1() Relations:=[]; // add the invers relations ac = ca = bd = db = 1 Append(Relations,[[a,c],[1]]); Append(Relations,[[c,a],[1]]); Append(Relations,[[b,d],[1]]); Append(Relations,[[d,b],[1]]); // add the relation a^{2}b^{-6} = aadddddd = 1 Append(Relations,[[a,a,d,d,d,d,d,d],[1]]); // add the relation (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1 with k = 3 Append(Relations,[[a,d,a,d,a,d,a,d,d,a,b,b,b,c,b],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther1(); GB:=NC.GB(Relations,31,1,100,1000);