> < ^ Date: Fri, 02 Nov 2001 14:37:10 +0100
> < ^ From: Burkhard Hoefling <b.hoefling@tu-bs.de >
> < ^ Subject:

Dear Radu Murgescu,

I am trying to compute the automorphism groups of some infinite groups
(free groups of small rank, in particular), but the AutomorphismGroup
function doesn't seem to work (I get an error message). Does the
argument to this function have to be a finite object? Any suggestions
of how I should deal with this would be appreciated.

as far as I know, at present GAP does not provide any algorithms for
computing automorphism groups of infinite groups. (The error message
you get is probably a "no method found" error, which indicates this).

However, the automorphism group of a free group of finite rank is
well-known. You can find explicit finite presentations (with usually
four or two generators, respectively) of these automorphism groups in
papers by Nielsen (Math. Ann. 91 (1924), 169-209) and B. H. Neumann
(Math. Ann. 107 (1932), 367-386). A student here is presently looking
at an implementation in GAP.

Please note that it depends very much on the type of questions you
have whether you can compute the answer with these finite
presentations (of infinite groups) in GAP.

Best regards,

Burkhard Höfling.
Dr. Burkhard Höfling                 Phone       (0531)  391 7526
Institut für Geometrie               Phone intl. +49 531 391 7526
Technische Universität               Fax         (0531)  391 8210
Pockelsstr. 14                       Fax   intl. +49 531 391 8210
38106 Braunschweig, Germany          WWW   www.tu-bs.de/~bhoeflin

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