Difference between revisions of "ApCoCoA-1:Other1 groups"
From ApCoCoAWiki
| Line 11: | Line 11: | ||
/*Use the ApCoCoA package ncpoly.*/ | /*Use the ApCoCoA package ncpoly.*/ | ||
| + | //K is congruent to 3 mod 6 | ||
| + | MEMORY.K:=3; | ||
// 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]; | ||
| Line 26: | Line 28: | ||
Append(Relations,[[a,a,d,d,d,d,d,d],[1]]); | Append(Relations,[[a,a,d,d,d,d,d,d],[1]]); | ||
| − | // add the relation (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1 | + | // add the relation (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1 |
| − | Append(Relations,[[a,d,a,d,a,d,a,d,d,a,b | + | Append(Relations,[[a,d,a,d,a,d,a,d,d,a,b^MEMORY.K,c,b],[1]]); |
| + | |||
Return Relations; | Return Relations; | ||
EndDefine; | EndDefine; | ||
Relations:=CreateRelationsOther1(); | Relations:=CreateRelationsOther1(); | ||
| − | + | Gb:=NC.GB(Relations,31,1,100,1000); | |
Revision as of 09:48, 23 September 2013
Description
This group has the following representation:
G = <a,b | a^{2}b^{-6} = (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1>
where k is congruent to 3 mod 6.
Reference
No reference available
Computation
/*Use the ApCoCoA package ncpoly.*/
//K is congruent to 3 mod 6
MEMORY.K:=3;
// a is invers to c and b is invers to d
Use ZZ/(2)[a,b,c,d];
NC.SetOrdering("LLEX");
Define CreateRelationsOther1()
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^{-6} = aadddddd = 1
Append(Relations,[[a,a,d,d,d,d,d,d],[1]]);
// add the relation (ab^{-1})^{3}ab^{-2}ab^{k}a^{-1}b = 1
Append(Relations,[[a,d,a,d,a,d,a,d,d,a,b^MEMORY.K,c,b],[1]]);
Return Relations;
EndDefine;
Relations:=CreateRelationsOther1();
Gb:=NC.GB(Relations,31,1,100,1000);
