> < ^ Date: Mon, 15 May 2000 19:10:57 -0400 (EDT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: derived and commutator subgroups

Dear Forum,

Laurent Bartholdi asked last week about `CommutatorSubgroup' for fp

so: since these L[n] are finitely generated, couldn't gap be able to
compute them? (and then, provide their index, etc)
and: why does derivedsubgroup() work,

`DerivedSubgroup' obtains the result (in a special method for fp groups) as
kernel of the homomorphism onto the largest abelian quotient, while
`CommutatorSubgroup' only has the generic method available which starts
collecting commutators. The problem with fp groups is the check,
whether a new commutator is contained in the subgroup spanned so far, which
fails for an infinite index subgroup spanned by only one commutator.

It is possible, however, to use an approach similar to `DerivedSubgroup' for
`CommutatorSubgroup' as well, computing the largest quotient in which the
one subgroup becomes central. (This is similar to a nilpotent quotient
algorithm.) There will be functionality in the next release which does this
(provided the index stays finite).
(If you need code for this now, just send me an email.)

> if there is an objection to
> working with
> infinite groups?
There is (or better: should be -- its always dangerous to promise everuthing
works as intended ...) no objection to working with infinite groups. However
at the moment extremely little functionality for subgroups of infinite index



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