> From GAP-Forum-Sender@dcs.st-and.ac.uk Mon Aug 19 16:00 BST 2002
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> X-Miles:        GAP Forum article 3750 accepted at 19 Aug 2002 15:45 +0100
> Date:           Mon, 19 Aug 2002 16:48:05 +0200
> From: Juergen Ecker <juergen@verdi.algebra.uni-linz.ac.at>
> To: Multiple recipients of list <GAP-Forum@dcs.st-and.ac.uk>
> Subject:        coset enumeration
> 
Dear GAP Forum,

Juergen Ecker wrote:

I have tried to work with the group

< p,q,r; p^4, p^2=q^3=(pq)^5, r^2=(rp)^4=p^2 >

in GAP. According to Zassenhaus' "Ueber endliche Fastkoerper" (On finite
nearfields), this is a group having <p,q>=SL(2,5) as a normal subgroup
of index 2.

This group is visibly an amalgamated free product of the subgroups <p,q>
and <p,r>, which have orders 120 and 16, with the amalgamated subgroup <p>
of order 4. So it is infinite. Maybe you have missed out some relations?
I would expect there to be relations involving both q and r, otherwise you
will get an amalgamated free product.

Derek Holt.

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