> < ^ Date: Thu, 09 May 2002 11:07:05 -0600 (MDT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: abelian factors of the kernel of a homomorphism

Dear GAP-Forum,

In 1998 Dimitrii Pasechnik asked:

> I have a homomorphism of a (big, possibly infinite) finitely
> presented group to a permutation group of degree few hundred.
> The image of homomorphism is McL (the MacLaughlin group)
> in its minimal permutation representation on 275 points.
> It is constructed by adding 2 extra relators to the original presentation
> It is known that G itself also admits a homomorphism onto a nonsplit
> extension 3^23.McL. We conjecture that the abelian invariants of
> the kernel of G->McL are just this 3^23.
> I would like to know the abelian factors of the kernel of this
> homomorphism.
> Is there a way of doing this in GAP now?

In 1998 this was impossible in GAP. Now, however, GAP 4.3 contains much
improved methods for working with finitely presented groups. Using these, I
have been able to show that there is indeed at least an homomorphism onto an
extension (3^104.3.3^21.3 x 3^104).McL.

The techniques used for this are descibed in a paper which recently appeared
in `Experimental Mathematics', 10 (2001), no.3, 369-381.
The web page
gives more information, in particular a transscript of the GAP calculations.

I would expect that the techniques used in the calculation might be of
interest also to other people working with finitely presented groups.

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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