> < ^ Date: Wed, 28 Jan 1998 18:04:09 +0100
> < ^ From: Dmitrii Pasechnik <d.pasechnik@twi.tudelft.nl >
> < ^ Subject: Re: abelian factors of the kernel of a homomorphism

Dear Forum members, dear Prof. Neubueser,

Let me clarify my question.
> Dear Forum,
> I have a homomorphism of a (big, possibly infinite) finitely
> presented group to a permutation group of degree few hundred.
> I would like to know the abelian factors of the kernel of this
> homomorphism.
> Is there a way of doing this in GAP now?
For subgroups of a finitely presented group of small index methods
such as RS and MTC are available, so the answer to your question
depends crucially on the size of your 'permutation group of degree few
hundred'. This of course can be determined by GAP using the well known
techniques for permutation groups. Please do this and contact us in
case the image of your homomorphisme turns out to be reasonably small,
then we could see if (and how best) the rest can be handled.
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 G.
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.

Unfortunately, so far I was not able to find a set of words in G itself
which would generate a subgroup of finite index >1.
Is there any way around this?

Thanks in advance

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