[GAP Forum] Question about obtaining the PIMs of a finite group algebra kG in a quick way and MeatAxe64

[Dima Pasechnik]

Dear all,
On Wed, Oct 21, 2020 at 09:34:02AM +0200, J??rgen M??ller wrote:
> Dear Bernhard,
> 
> > Rumors told that there is MeatAxe64, but I don't have many pieces of
> > information about this yet. Is it freely available?
> 
> About this, you probably best ask Richard Parker himself.

There is an easy to install fork of meataxe(64?)
https://github.com/simon-king-jena/SharedMeatAxe
used in SageMath (https://sagemath.org)

Just in case,
Dima

> 
> > I don't want to chop the regular module, and I am speaking of groups of
> > order approximately between 20 000 and 1000 000.
> 
> Looking for PIMs is a matter of spinning up vectors (in MeatAxe language)
> in suitable modules, rather than chopping. But PIMs typically are `large??? 
> modules, whose dimension is comparable to the group order, so that you 
> might have to deal with modules `close??? to the regular module.
> 
> Of course, spinning in the regular module in principle yields a general 
> algorithm, which even might be feasible in your cases, since the regular 
> module is a permutation module.
> 
> But, depending on the example under consideration, you might be able 
> to do better: for example, if G is p-solvable, then the 1-PIM is just the 
> permutation module on the cosets of Hall p???-subgroup.
> 
> > Later, I would like to use the obtained result tomake further computations
> > with other kG-modules, as well.
> 
> Doing sophisticated computations with modules of dimension 10^6
> might easily be prohibitive.  So, what precisely do you want to know 
> about the PIMs? (For example, if you are interested in Ext groups 
> between simple modules, there are other ways to tackle that.)
> 
> Hope this helps.
> 
> Best wishes, J??rgen M??ller
> 
> > Am 21.10.2020 um 00:09 schrieb Bernhard Boehmler <bernhard.boehmler at googlemail.com>:
> > 
> > Dear GAP forum,
> > 
> > let G be a finite group and k be a finite field where char(k)=p divides the
> > order of G.
> > 
> > I would like to kindly ask you the following question:
> > 
> > Is there an algorithm (freely available or already implemented in GAP4)
> > that can find in a relatively quick way the PIMs of kG for relatively big
> > groups G?
> > 
> > I wouldn't care if it took a few days, but a few months would probably be
> > too time consuming.
> > 
> > I don't want to chop the regular module, and I am speaking of groups of
> > order approximately between 20 000 and 1000 000.
> > 
> > Later, I would like to use the obtained result tomake further computations
> > with other kG-modules, as well.
> > 
> > Rumors told that there is MeatAxe64, but I don't have many pieces of
> > information about this yet. Is it freely available?
> > 
> > Any help is appreciated.
> > 
> > Thanks in advance.
> > 
> > Kind regards,
> > Bernhard Boehmler
> > _______________________________________________
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> > Forum at gap-system.org
> > https://mail.gap-system.org/mailman/listinfo/forum
> 
> 
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