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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

Dima

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