# ApCoCoA-1:Mathieu11 group

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### Mathieu group M {11}

#### Computation

``` /*Use the ApCoCoA package ncpoly.*/

Use ZZ/(2)[a,b];
NC.SetOrdering("LLEX");

Define CreateRelationsMathieuM11()
Relations:=[];

// add the relation a^2 = 1
Append(Relations,[[a,a],[1]]);
// add the relation b^4 = 1
Append(Relations,[[b,b,b,b],[1]]);

//add the relation (ab)^11 = 1
Append(Relations,  [[a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b,a,b],[1]]);

//add the relation (ab^2)^6 = 1
Append(Relations,[[a,b,b,a,b,b,a,b,b,a,b,b,a,b,b,a,b,b],[1]]);

//add the relation ababab^{-1}abab^2ab^{-1}abab^{-1}ab^{-1} = 1
Append(Relations,[[a,b,a,b,a,b,b,b,a,b,a,b,b,a,b,b,b,a,b,a,b,b,b,a,b,b,b],[1]]);

Return Relations;
EndDefine;

Relations:=CreateRelationsMathieuM11();
Relations;

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

#### Example in Symbolic Data Format

``` <FREEALGEBRA createdAt="2014-03-26" createdBy="strohmeier">
<vars>a,b</vars>
<uptoDeg>27</uptoDeg>
<basis>
<ncpoly>a*a-1</ncpoly>
<ncpoly>b*b*b*b-1</ncpoly>
<ncpoly>(a*b)^11-1</ncpoly>
<ncpoly>(a*b*b)^6-1</ncpoly>
<ncpoly>a*b*a*b*a*b*b*b*a*b*a*b*b*a*b*b*b*a*b*a*b*b*b*a*b*b*b-1</ncpoly>
</basis>
<Comment>The partial LLex Gb has 15 elements</Comment>
<Comment>Mathieu group_M_{11}</Comment>
</FREEALGEBRA>
```