# ApCoCoA-1:Other4 groups

From ApCoCoAWiki

Revision as of 13:43, 18 September 2013 by F lorenz (talk | contribs) (New page: === <div id="Other4_groups">Other groups</div> === ==== Description ==== This group has the following representation: G = <a,b | a^2 = b^3 = (abab...)

#### Description

This group has the following representation:

G = <a,b | a^2 = b^3 = (ababab^{2})^{3} = 1>

The number of elements of the Groebner-Basis is 111554.

#### Reference

No reference available

#### Computation

/*Use the ApCoCoA package ncpoly.*/ Use ZZ/(2)[a,b]; NC.SetOrdering("LLEX"); Define CreateRelationsOther4() Relations:=[]; // add the relations a^2 = b^3 = 1 Append(Relations,[[a,a],[1]]); Append(Relations,[[b,b,b],[1]]); // add the relation (ababab^{2})^{3} = 1 Append(Relations,[[a,b,a,b,a,b,b,a,b,a,b,a,b,b,a,b,a,b,a,b,b],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther4(); GB:=NC.GB(Relations); Size(GB);