# Difference between revisions of "ApCoCoA-1:Other11 groups"

From ApCoCoAWiki

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MEMORY.R := 3; | MEMORY.R := 3; | ||

MEMORY.N := 4; | MEMORY.N := 4; | ||

+ | |||

// x is invers to z, t has an implicit invers (Relation: t^{n} = 1) | // x is invers to z, t has an implicit invers (Relation: t^{n} = 1) | ||

Use ZZ/(2)[x,t,z]; | Use ZZ/(2)[x,t,z]; | ||

NC.SetOrdering("LLEX"); | NC.SetOrdering("LLEX"); | ||

+ | |||

Define CreateRelationsOther11() | Define CreateRelationsOther11() | ||

Relations:=[]; | Relations:=[]; | ||

Line 42: | Line 44: | ||

EndFor; | EndFor; | ||

Append(Relations,[RelationBuffer1,RelationBuffer2]); | Append(Relations,[RelationBuffer1,RelationBuffer2]); | ||

+ | |||

Return Relations; | Return Relations; | ||

EndDefine; | EndDefine; | ||

Relations:=CreateRelationsOther11(); | Relations:=CreateRelationsOther11(); | ||

− | + | Gb:=NC.GB(Relations,31,1,100,1000); |

## Revision as of 02:37, 24 September 2013

#### 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]); Return Relations; EndDefine; Relations:=CreateRelationsOther11(); Gb:=NC.GB(Relations,31,1,100,1000);