> < ^ Date: Thu, 15 Nov 2001 09:05:22 -0700 (MST)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: presentation of a large group..

Dear Gap Forum,


I have a large group, a quotient of an infinite group on five
generators. I have a permutation representation of it on 50 points,
and would like to find a presentation for it.

The order of the group is 943718400 = 2^17 . 7200. I know the
presentation of the (non-normal) subgroup of order 7200 generated
by 4 of the generators. I'm using the two-stage algorithm provided
in GAP4r2, but so far it's taken 3 days on a Pentium 550 under

Any advice on how to tackle this kind of problem more efficiently?

Based on the groups order, I'd suspect that the group contains a large
solvable part. The two-stage algorithm is not very suited for large groups
of this type. Instead, `IsomorphismFpGroup' (which works along a composition
series) is likely to work better, however it choses a larger generator set.
(The `Range' of the isomorphism is an FpGroup, `RelatorsOfFpGroup' for this
returns a set of relators.)

Both the two-stage algorithm and `IsomorphismFpGroup' will been improved in
the forthcoming release GAP 4.3.
If the presentation you obtained in GAP 4.2 is too big for your purposes,
feel free to send us the permutation representation
(gap-trouble@dcs.st-and.ac.uk) and we can try it out in our development

Best regards,

Alexander Hulpke

-- Colorado State University, Department of Mathematics,
Weber Building, Fort Collins, CO 80523, USA
email: hulpke@math.colostate.edu, Phone: ++1-970-4914288

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