[GAP Forum] best way to work with modules under group rings

[Will Chen]

Hi all,

Given a finite metabelian group G, let A be its abelianization, and G' be
its derived subgroup. I would like to get a handle on G' as an A-module.
I'm happy to work with either Z[A]-modules or (Z/n)[A]-modules.

For example, I would like to be able to:

1. Compute A-module generators for G'
2. Construct A-module homomorphisms between A-modules by specifying where
they send generators.
3. Compute kernels and images of A-module homomorphisms, as well as
constructing submodules and quotient modules...
4. Compute the groups of units of finite quotients of Z[A]...

What is the best way to do such things in GAP?

- Will


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William Chen
NSF Postdoctoral Fellow, Department of Mathematics
McGill University,
Montreal, Quebec, H3A 0B9
oxeimon at gmail.com