# Difference between revisions of "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],]);
Append(Relations,[[z,x],]);

// add the relation t^{n} = 1
RelationBuffer0:=[];
For Index0:=1 To MEMORY.N Do
Append(RelationBuffer0,t);
EndFor;
Append(Relations,[RelationBuffer0,]);

// 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]);
Return Relations;
EndDefine;

Relations:=CreateRelationsOther11();
GB:=NC.GB(Relations,31,1,100,1000);
```