[GAP Forum] ConjugacyClasses function question

[Stefan Kohl]

Dear Forum,

Linda Cupples asked:

> I've been trying to find a way to determine the elements in each of the
> conjugacy classes that is given by gap,
>
> My code is pretty much,
>
> F:=FreeGroup("a","b");
> <free group on the generators [ a, b ]>
> a:=F.1;;b:=F.2;;
> G:=F/[a^4,b^4,(a*b)^2,(a^3*b)^2];
>
> ConjugacyClasses(G);
> [ <identity ...>^G, a^G, b^G, a^2*b^2^G, a^2^G, a*b^G, a^3^G, a^2*b^G,
> b^2^G, a^3*b^G ]
>
> List(ConjugacyClasses(G), Size);
> [ 1, 2, 2, 1, 1, 2, 2, 2, 1, 2 ]
>
> Is it possible to retrive the actual elements in each of the conjugacy
> classes of size 2? Instead of the output "a^G", a and its conjugate?

The answer is yes. -- Just apply `AsList' to the conjugacy classes:

gap> List(ConjugacyClasses(G),AsList);
[ [ <identity ...> ], [ a, b^-1*a*b ], [ b, a^-1*b*a ], [ a^2*b^2 ], [ a^2 ],
  [ a*b, b*a ], [ a^3, b^-1*a^3*b ], [ a^2*b, a*b*a ], [ b^2 ],
  [ a^3*b, a^2*b*a ] ]

Hope this helps,

    Stefan Kohl