ApCoCoA-1:Other13 groups

Other groups

Description

This group has the following finite representation:

G = <x,y | x^2 = xy^{a}xy^{b}xy^{c}xy^{d} = 1>

Reference

No reference available

Computation

 /*Use the ApCoCoA package ncpoly.*/
 
 // Note that a,b,c,d >= 1
 MEMORY.A := 3;
 MEMORY.B := 3;
 MEMORY.C := 4;
 MEMORY.D := 5;

 // y is invers to z, the invers element of x follows directly from the relation x^2 = 1
 Use ZZ/(2)[x,y,z];
 NC.SetOrdering("LLEX");
 Define CreateRelationsOther13()
   Relations:=[];
   
   // add the relation of the invers elements yz = zy = 1
   Append(Relations,[[y,z],[1]]);
   Append(Relations,[[z,y],[1]]);
   
   // add the relation x^2 = 1
   Append(Relations,[[x,x],[1]]);
   
   // add the relation xy^{a}xy^{b}xy^{c}xy^{d}
   Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]);

   Return Relations;
 EndDefine;
 
 Relations:=CreateRelationsOther13();
 Gb:=NC.GB(Relations,31,1,100,1000);