ApCoCoA-1:Other4 groups

Other groups

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);