[GAP Forum] fp groups

[Alexander Konovalov]

Dear Vahid,

On 26 Aug 2008, at 22:40, Vahid Dabbaghian wrote:

> Dear GAP Forum,
>
> In the following example I have computed an isomorphism from a  
> finite group
> G to a finitely presented group and I would like to get the list of  
> powers
> of generators of the elements in the finitely presented group. Does  
> anybody
> know how can I do that? For example how can I get
> [ [F2, -1], [F1, -1], [F2, 1], [F1, -1], [F2, 1], [F3, -1] ]
> corresponding to
> F2^-1*F1^-1*F2*F1^-1*F2*F3^-1.
>
> gap> U:=[ (1,2), (1,2,3,4,5), (5,6) ];;
> gap> G:=Group(U);;
> gap> a:=IsomorphismFpGroupByGenerators(G,U);
> [ (1,2), (1,2,3,4,5), (5,6) ] -> [ F1, F2, F3 ]
> gap> z:=Random(G)^a;
> F2^-1*F1^-1*F2*F1^-1*F2*F3^-1

You may use ExtRepOfObj. For example:

gap> z:=Random(G)^a;
F3*F2*F1^-1*F2^-2*F1*F2
gap> ExtRepOfObj(z);
[ 3, 1, 2, 1, 1, -1, 2, -2, 1, 1, 2, 1 ]

See section 35.7 "The External Representation for Associative Words"
of the Reference Manual for the documentation.

Best wishes,
Alexander