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);

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>