Dear Toni,

you wrote a little while ago:
>
> Let F be the free group of rank 4 freely generated
> by a1,a2,a3,a4. Let w=a1^2*a2^2*a3^2*a4^2.
> Proposition 5.7 (due to McCool) of Lyndon and Schupp
> asserts that there is an effective procedure for finding
> a finite presentation for the stabilizer in Aut(F)
> of the cyclic word (w), where (w) is the set of cyclically
> reduced conjugates of w. In this particular case, can
> anyone tell me what the finite presentation for the
> stabilizer is? Or, maybe could you tell me if some software
> (for example, GAP) can be used to compute it?

I don't know the answer to your first question and only a partial answer to
the second. There is no procedure in GAP for computing the stabiliser in
Aut(F) of a cyclic word.

After looking through the relevant part of Lyndon/Schupp I am sure that such a
procedure could be written in GAP. I would very much welcome anyone who would
like to do that and offer assistance with the programming. If you find out
anything more or if you want to do the programming yourself, I would be
interested to know.

All the best, Werner Nickel.