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
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