ApCoCoA-1:Other11 groups

Other groups

Description

This group has the following finite representation:

G = <x,t | xt^{r} = tx^{r},t^{n} = 1>

for r >= 1 and n >= 2

Reference

No reference available

Computation of G

 /*Use the ApCoCoA package ncpoly.*/
 
 // Note that r >= 1 and n >= 2
 MEMORY.R := 3;
 MEMORY.N := 4;
 // x is invers to z, t has an implicit invers (Relation: t^{n} = 1)
 Use ZZ/(2)[x,t,z];
 NC.SetOrdering("LLEX");
 Define CreateRelationsOther11()
   Relations:=[];
   
   // add the invers relations xz = zx = 1
   Append(Relations,[[x,z],[1]]);
   Append(Relations,[[z,x],[1]]);
   
   // add the relation t^{n} = 1
   RelationBuffer0:=[];
   For Index0:=1 To MEMORY.N Do
     Append(RelationBuffer0,t);
   EndFor;
   Append(Relations,[RelationBuffer0,[1]]);
   
   // add the relation xt^{r} = tx^{r}
   RelationBuffer1:=[];
   RelationBuffer2:=[];
   Append(RelationBuffer1,x);
   Append(RelationBuffer2,t);
   For Index1:= 1 To MEMORY.R Do
     Append(RelationBuffer1,t);
     Append(RelationBuffer2,x);
   EndFor;
   Append(Relations,[RelationBuffer1,RelationBuffer2]);
   Relations;
   Return Relations;
 EndDefine;
 
 Relations:=CreateRelationsOther11();
 GB:=NC.GB(Relations,31,1,100,1000);