# Difference between revisions of "ApCoCoA-1:Other13 groups"

From ApCoCoAWiki

(New page: === <div id="Other13_groups">Other groups</div> === ==== Description ==== This group has the following finite representation: G = <x,y | x^2 = xy^{...) |
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/*Use the ApCoCoA package ncpoly.*/ | /*Use the ApCoCoA package ncpoly.*/ | ||

− | // Note that a,b >= 1 | + | // Note that a,b,c,d >= 1 |

MEMORY.A := 3; | MEMORY.A := 3; | ||

MEMORY.B := 3; | MEMORY.B := 3; | ||

MEMORY.C := 4; | MEMORY.C := 4; | ||

MEMORY.D := 5; | MEMORY.D := 5; | ||

+ | |||

// y is invers to z, the invers element of x follows directly from the relation x^2 = 1 | // y is invers to z, the invers element of x follows directly from the relation x^2 = 1 | ||

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

Line 31: | Line 32: | ||

// add the relation xy^{a}xy^{b}xy^{c}xy^{d} | // add the relation xy^{a}xy^{b}xy^{c}xy^{d} | ||

Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]); | Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]); | ||

+ | |||

Return Relations; | Return Relations; | ||

EndDefine; | EndDefine; | ||

Relations:=CreateRelationsOther13(); | Relations:=CreateRelationsOther13(); | ||

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

## Revision as of 02:42, 24 September 2013

#### Description

This group has the following finite representation:

G = <x,y | x^2 = xy^{a}xy^{b}xy^{c}xy^{d} = 1>

#### Reference

No reference available

#### Computation

/*Use the ApCoCoA package ncpoly.*/ // Note that a,b,c,d >= 1 MEMORY.A := 3; MEMORY.B := 3; MEMORY.C := 4; MEMORY.D := 5; // y is invers to z, the invers element of x follows directly from the relation x^2 = 1 Use ZZ/(2)[x,y,z]; NC.SetOrdering("LLEX"); Define CreateRelationsOther13() Relations:=[]; // add the relation of the invers elements yz = zy = 1 Append(Relations,[[y,z],[1]]); Append(Relations,[[z,y],[1]]); // add the relation x^2 = 1 Append(Relations,[[x,x],[1]]); // add the relation xy^{a}xy^{b}xy^{c}xy^{d} Append(Relations,[[x,y^(MEMORY.A),x,y^(MEMORY.B),x,y^(MEMORY.C),x,y^(MEMORY.D)],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther13(); Gb:=NC.GB(Relations,31,1,100,1000);