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In connection with Thierry Dana-Picard's question about finding Loewy series,

I have written several GAP routines which handle group representations which

in particular will compute the Loewy series of any representation of a

p-group in characteristic p (and more generally the Loewy series of the

largest quotient of a module all of whose composition factors are trivial).

The algorithm I use is simply to multiply repeatedly by the augmentation

ideal. The trouble with this approach if one is interested in the Loewy

series of the group ring is that the regular representation has a large

dimension, and for reasons of time and storage the problem may become

computationally unfeasible that way. Jenning's theorem could be the better

approach!

On the topic of representation theory within GAP, I have the impression

that this side of things has been somewhat neglected so far. The meataxe

is implemented, but I have other goals in mind to do with creating software

to complement this. For example, the meataxe would not be so good for

analyzing the structure of modules for p-groups in characteristic p, but

algorithms based upon the computation of fixed points are very effective in

this situation. It is a long-term project for me to expand what software

I have, and to put it into a publicly acceptable state. Right now, for

example, it does not properly conform to the object-oriented style of GAP,

and it is not adequately tested. At this point I would be happy to hear of

others writing similar software (some I already know of). My general aim

is to have a package which computes Loewy series reasonably, will extract

a quotient in the Loewy series of a p-group as a representation of its

normalizer in a larger group (for example), will compute relative traces

between modules of fixed points, and such similar things.

Peter Webb

webb@math.umn.edu

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