Dear Robert Heffernan,
I am dealing with groups constructed in this manner:
F:=FreeGroup("x","y","z");G:=F/rels;
where rels is some list of relations in terms of x,y and z.
If the group is large GAP seems to have trouble constructing the
groupof automorphisms of G.
I understand that doing this:G:=Image(IsomorphismPermGroup
(G));would give me a representation of the group that GAP can deal
witheasily (and easily compute Aut G, etc.), but I want to look at
theautomorphisms in terms of the generators x,y and z above.
That is not a contradiction. Compute the automorphism group for the
permutation representation and then pull the generators back to the
finitely presented group.
Concretely, if
phi:=IsomorphismPermGroup(G);
P:=Image(phi);
A:=AutomorphismGroup(P);
you can do
List(GeneratorsOfGroup(A),a->GroupHomomorphismByImagesNC
(G,G,GeneratorsOfGroup(G),
List(GeneratorsOfGroup(G),x->PreImagesRepresentative(phi,Image
(a,Image(phi,x)))));
to get generators of the automorphism group in terms of x,y and z.
Best,
Alexander Hulpke
-- Colorado State University, Department of Mathematics,
Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA
email: [EMAIL PROTECTED], Phone: ++1-970-4914288
http://www.math.colostate.edu/~hulpke
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