Dear GAP Forum,
On Mar 15, 2007, at 1:50 AM, Michael Fridman wrote:
I have a question regarding the Reidemeister-Schreier method. I have a
finitely presented group G and a set of the schreier generators of a
subgroup H. so using "PresentationSubgroup " I found a presentation
of the
subgroup H. However, I need to know how the generators of the
subgroup H
(when they are calculated using the RMS method) are expressed in
terms of
the generators of G. how can do it?
The easiest way to do so is to use `IsomorphismFpGroup' applied to H.
This will do a Reidemeister-Schreier rewriting (and Tietze
transformations) to obtain a presentation for H. The `Range' of this
homomorphism is the newly presented group. You can use the
homomorphism to rewrite elements between H<=G and the new group
isomorphic to H.
(If you wanted to do this with PresentationSubgroup you would have to
do the translation by hand. See the code in lib/ghomfp.gi.)
He also asked:
Given a finitely presented group G, I need
to find all the surjective homomorphisms to the symmetric group of n
elements (when n is given). Can I use GAP to do it?
I assume you want one n at a time. You could use `GQuotients' to do
this. (However be aware that this is likely to fail if your n gets
too big. n=10 should be doable. n=100 is likely out of range.)
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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