ApCoCoA-1:Other7 groups

Other Groups

Description

The next group has the order |G| = 9216 and the following finite representation:

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

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 CreateRelationsOther7()
   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^{-3} = 1
   Append(Relations,[[a,a,d,d,d],[1]]);
   
   // add the relation (ababa^{2}ab^{2})^2=  1
   Append(Relations,[[a,b,a,b,a,a,a,b,b,a,b,a,b,a,a,a,b,b],[1]]);
   
   Return Relations;
 EndDefine;
 
 Relations:=CreateRelationsOther7();
 GB:=NC.GB(Relations,31,1,100,1000);

Example in Symbolic Data Format

 <FREEALGEBRA createdAt="2014-01-20" createdBy="strohmeier">
 	<vars>a,b,c,d</vars>
 	<uptoDeg>14</uptoDeg>
 	<basis>
 	<ncpoly>a*c-1</ncpoly>
 	<ncpoly>c*a-1</ncpoly>
 	<ncpoly>b*d-1</ncpoly>
 	<ncpoly>d*b-1</ncpoly>
 	<ncpoly>a*a*d*d*d-1</ncpoly>
 	<ncpoly>(a*b*a*b*a*a*a*b*b)^2-1</ncpoly>
 	</basis>
 	<Comment>The partial LLex Gb has 199 elements</Comment>
 	<Comment>Other_groups7</Comment>
 </FREEALGEBRA>