> From GAP-Forum-Sender@dcs.st-and.ac.uk Mon Aug 19 16:00 BST 2002 > X-Authentication-Warning: chrystal.mcs.st-and.ac.uk: miles set sender to GAP-Forum-Sender@dcs.st-and.ac.uk using -f > 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 <firstname.lastname@example.org> > 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.