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);
