# Difference between revisions of "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],]);
Append(Relations,[[b^3],]);

// 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],]);

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>
```