> < ^ Date: Wed, 08 Sep 1999 18:00:53 +0200 (CEST)
> < ^ From: Thomas Breuer <Thomas.Breuer@Math.RWTH-Aachen.DE >
< ^ Subject: Re: Units in grouprings - Ann Dooms' question

Dear GAP Forum,

last week Alexander B. Konovalov forwarded a question of Ann Dooms to you.

I'm a student at the university of Brussels in Belgium. I'm in my fourth
and last year and so I have to make a thesis. One of my possible subjects
is units of grouprings (this subject was given by Erik Jespers, maybe you
know him). Jespers wrote an article about units in \ZS_{3}, which was very
technical and done without the use of computer. I think it must be
possible to do it with GAP and on the site of GAP I discovered your email
address. I see that you are already thinking about D_{8}. Now I'm
wondering if there is already an algorithm built-in in GAP. Hoping you can
help me,

Without knowing what calculations with integral group rings Ann
has in mind (I would be interested in the details),
I can state only that currently GAP does not provide
special functionality for (groups of) units in group rings.
Mainly the arithmetics for group ring elements is available,
so one can add, multiply, invert etc. elements in group rings.
(Currently the function for computing the inverse of an element
in an integral group ring may run into an error,
this will be fixed with the next bugfix.)

For group rings of small groups,
it may be possible to answer questions by solving
linear equation systems.
In the case of group rings over the integers,
the problem with this approach is that the implementation
of Z-modules is not yet complete.
I hope to improve this situation until the release of GAP 4.2.

Sorry that I do not have better news.

Kind regards,
Thomas Breuer

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