Difference between revisions of "ApCoCoA-1:Other5 groups"
From ApCoCoAWiki
| Line 15: | Line 15: | ||
Use ZZ/(2)[a,b,c,d]; | Use ZZ/(2)[a,b,c,d]; | ||
NC.SetOrdering("LLEX"); | NC.SetOrdering("LLEX"); | ||
| − | Define | + | Define CreateRelationsOther5() |
Relations:=[]; | Relations:=[]; | ||
| Line 33: | Line 33: | ||
EndDefine; | EndDefine; | ||
| − | Relations:= | + | Relations:=CreateRelationsOther5(); |
GB:=NC.GB(Relations,31,1,100,1000); | GB:=NC.GB(Relations,31,1,100,1000); | ||
| Line 43: | Line 43: | ||
Use ZZ/(2)[a,b,c,d]; | Use ZZ/(2)[a,b,c,d]; | ||
NC.SetOrdering("LLEX"); | NC.SetOrdering("LLEX"); | ||
| − | Define | + | Define CreateRelationsOther6() |
Relations:=[]; | Relations:=[]; | ||
| Line 61: | Line 61: | ||
EndDefine; | EndDefine; | ||
| − | Relations:= | + | Relations:=CreateRelationsOther6(); |
GB:=NC.GB(Relations,31,1,100,1000); | GB:=NC.GB(Relations,31,1,100,1000); | ||
Revision as of 14:34, 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 CreateRelationsOther5()
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:=CreateRelationsOther5();
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 CreateRelationsOther6()
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:=CreateRelationsOther6();
GB:=NC.GB(Relations,31,1,100,1000);
