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

From ApCoCoAWiki

(New page: === <div id="Other5_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,t | xt^{r} = tx...) |
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− | === <div id=" | + | === <div id="Other11_groups">[[:ApCoCoA:Symbolic data#Other_groups|Other groups]]</div> === |

==== Description ==== | ==== Description ==== | ||

This group has the following finite representation: | This group has the following finite representation: |

## Revision as of 15:39, 18 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]); Relations; Return Relations; EndDefine; Relations:=CreateRelationsOther11(); GB:=NC.GB(Relations,31,1,100,1000);