# Difference between revisions of "ApCoCoA-1:Other5 groups"

From ApCoCoAWiki

(New page: === <div id="Other5_groups">Other groups</div> === ==== Description ==== The first group, denoted by G, has an order |G| = 4224 and can be represent...) |
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==== Computation of H ==== | ==== Computation of H ==== | ||

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+ | /*Use the ApCoCoA package ncpoly.*/ | ||

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// a is invers to c and b is invers to d | // a is invers to c and b is invers to d | ||

Use ZZ/(2)[a,b,c,d]; | Use ZZ/(2)[a,b,c,d]; |

## Revision as of 14:06, 18 September 2013

#### Description

The first group, denoted by G, has an order |G| = 4224 and can be represented as:

G = <a,b | a^{2}b^{-4} = (ababab^{3})^{2} = 1>

The second group, denoted by H, is also solvable and has the following representation:

H = <a,b | a^{2}b^{4} = (ababab^{3})^{2} = 1>

#### Reference

#### Computation of G

/*Use the ApCoCoA package ncpoly.*/ // a is invers to c and b is invers to d Use ZZ/(2)[a,b,c,d]; NC.SetOrdering("LLEX"); Define CreateRelationsOther4() Relations:=[]; // add the invers relations ac = ca = bd = db = 1 Append(Relations,[[a,c],[1]]); Append(Relations,[[c,a],[1]]); Append(Relations,[[b,d],[1]]); Append(Relations,[[d,b],[1]]); // add the relation a^{2}b^{-4} = 1 Append(Relations,[[a,a,d,d,d,d],[1]]); // add the relation (ababab^{3})^{2} = 1 Append(Relations,[[a,b,a,b,a,b,b,b,a,b,a,b,a,b,b,b],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther4(); GB:=NC.GB(Relations,31,1,100,1000);

#### Computation of H

/*Use the ApCoCoA package ncpoly.*/ // a is invers to c and b is invers to d Use ZZ/(2)[a,b,c,d]; NC.SetOrdering("LLEX"); Define CreateRelationsOther4() Relations:=[]; // add the invers relations ac = ca = bd = db = 1 Append(Relations,[[a,c],[1]]); Append(Relations,[[c,a],[1]]); Append(Relations,[[b,d],[1]]); Append(Relations,[[d,b],[1]]); // add the relation a^{2}b^{4} = 1 Append(Relations,[[a,a,b,b,b,b],[1]]); // add the relation (ababab^{3})^{2} = 1 Append(Relations,[[a,b,a,b,a,b,b,b,a,b,a,b,a,b,b,b],[1]]); Return Relations; EndDefine; Relations:=CreateRelationsOther4(); GB:=NC.GB(Relations,31,1,100,1000);