Dear GAP Forum members,

Some of you may just have received three times a truncated version of
this letter. I apologize and hope that this time I will come to terms
with my mailer.

Walter M. Potter asked in the Forum:

GAPers:

I expect that many of the algorithms developed for GAP have been
published in journal articles. I'm interested in learning more about
those algorithms. Would it be useful to look at the code for GAP?
Does any one have any good references?

I'm also looking at the literature.

Thanks, Walt

Walter M. Potter

Department of Mathematics and Computer Science
Southwestern University
Georgetown, Texas
(512) 863 1609

This is a request that 'GAPers' enjoy to see - and hate to answer.

Enjoy to see, because we would like to see algorithmic aspects become
part of the standard knowledge on group theory.

Hate to answer, because there is no easy answer. There is no general
textbook summarizing the main algorithmic methods used in a system
such as GAP, and even the GAP manual has only occasional and marginal
pointers to relevant publications on algorithmic methods. We know that
this is a serious deficiency, and that we ought to do a lot more in
this direction. The only excuse is that the development of the system
(by a fairly small team) just has had precedence so far.

There is a large number of publications on algorithms in
Computational group theory, but no good guide through it.

A first help may be to point to a few survey articles:

General overviews

A. Seress, An introduction to computational group theory.
Notices AMS 44 (19970, 671 -679.

J.N. An invitation to computational group theory.
Proceedings Groups 93 - Galway/St Andrews, Cambridge Univ. Press 1995.

For methods for finitely presented groups the book

C.C. Sims, Computation with Finitely presented Groups.
Cambridge Univ. press, 1994.

For some new methods mainly for permutation and matrix groups:

W.M. Kantor, Simple groups is computational group theory.
Proc. ICM, Berlin 1998 II, 77 -86.

For methods in representation theory:

K. Lux, H. Pahlings, Computational aspects of representation theory
of finite groups.
Progress in Mathematics, 95 (1991) 37 - 64. Birkhaeuser 1991.

In each of these you can find further pointers, in particular to
several proceedings and special issues of JSC devoted to the topic.
Certain areas are not covered by more recent surveys, e.g. the
methods for polycyclically presented groups, but the general surveys
give at least some pointers also to these.

As far as I know there are two textbooks in preparation on permutation
group methods by A. Seress and on representation theory methods by
H. Pahlings.

I will take the letter of Walter Potter as an incentive to discuss
with the members of the GAP team how we can at least partially fulfill
the justified request to get to know more about the mathematical
background of GAP.

Joachim Neubueser