> < ^ Date: Tue, 13 May 2003 18:08:59 +0200
< ^ From: Steve Linton <sal@dcs.st-and.ac.uk >
> < ^ Subject: Re: maximal subgroups

Dear GAP Forum,

Ahmad Erfanian asked:

I would like to use the function " ConjugacyClassesMaximalSubgroups " in
Gap, for groups PSL(5,2), PSL(6,2), PSL(7,2). But it seems that there is a
problem for running time or something else. I will be more grateful for any
help or comments.

As Dima Pasechnik has already said, these are rather large groups on which to
perform this sort of computation directly using general purpose machinery.

On the other hand, maximal subgroups of classical groups (including PSL) are
described by a theorem of Aschbacher, see:

Aschbacher, M.
Invent. Math. 76 (1984), no. 3, 469--514.
20G40 (20D05)

or the book of Kleidman and Liebeck

On the maximal subgroups of the finite classical groups.P. Kleidman\ and\ M.
Liebeck, {\it The subgroup structure of the finite classical groups},
Cambridge Univ. Press, Cambridge, 1990; MR 91g:20001

With this information it should not be too hard to write a GAP program to find
all the maximal subgroups up to conjugacy.

Steve Linton	School of Computer Science  &
      Centre for Interdisciplinary Research in Computational Algebra
	     University of St Andrews 	 Tel   +44 (1334) 463269
http://www.dcs.st-and.ac.uk/~sal	 Fax   +44 (1334) 463278   

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