> < ^ Date: Tue, 27 Jun 2000 15:04:03 -0400 (EDT)
> < ^ From: Alexander Hulpke <hulpke@math.colostate.edu >
< ^ Subject: Re: Reidemeister

Dear Gap-Forum,

let me try to answer the questions posed by Davide Ferrario as far as I feel
competent:

> 1. Is there a way to use the function DoubleCosets in a smart way (that
> is, check first that R(f) is finite)? I argue that a good starting point
If both subgroups have finite index, it would be relatively easy to add a
method that computes double coset representatives. Let me know if this would
Otherwise the existing code always assumes that the full group is finite.

> should be to consider polycyclic groups: How can I get more details on the
> (undocumented) function DoubleCosetsPcGroup?
`DoubleCosetsPcGroup' is based on notes of a talk by Michael Slattery in
1992 in Oberwolfach. I have been told, that a paper describing this
algorithm is to be published in J.Symb.Comp., but I don't have details. (If
you are able to read German -- there is a description in section 2.5.3 of my
Diploma thesis which you find at the first link at
http://www.math.ohio-state.edu/~ahulpke/publ.html)
I can't see a reason why this algorithm would fail in the infinite case,
however the implementation (e.g. the groups act only via their generators and
not the generators' inverses) implicitly assumes finiteness in a couple of
places.

> In any case, I found out that
> DirectProduct() does not seem to work for PcGroups (or maybe I am doing
> something wrong).
I'm a bit surprised. The direct product construction should work. Could you
send us the input that causes the problem?

> 3. Assume H is a fully invariant subgroup of G. What is the best way to
> define the restricted endomorphism f_H:H --> H and the endomorphism
> induced on the quotient F:G/H --> G/H ?
I don't know whether this is the best way -- I'm using `RestrictedMapping'
in the first case (though it does not restrict the codomain). For
automorphisms there is `InducedAutomorphism' in grppclat.gi, it should be
easy to adapt the code for endomorphisms.

Best regards,

Alexander Hulpke

-- The Ohio State University, Department of Mathematics,
231W 18th Avenue, Columbus, OH 43210, USA
email: ahulpke@math.ohio-state.edu, Phone: ++1-614-688-3175