ApCoCoA-1:Other4 groups
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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^2],[1]]); Append(Relations,[[b^3],[1]]); // add the relation (ababab^{2})^{3} = 1 Append(Relations,[[a,b,a,b,a,b^2,a,b,a,b,a,b^2,a,b,a,b,a,b^2],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther4(); Gb:=NC.GB(Relations); Size(Gb);
Example in Symbolic Data Format
<FREEALGEBRA createdAt="2014-01-20" createdBy="strohmeier"> <vars>a,b</vars> <basis> <ncpoly>a*a-1</ncpoly> <ncpoly>b*b*b-1</ncpoly> <ncpoly>(a*b*a*b*a*b*b)^3-1</ncpoly> <Comment>relation:(ababab^{2})^{3} = 1 </Comment> </basis> <Comment>Other_groups4</Comment> </FREEALGEBRA>