[GAP Forum] Resolution

[Ellis, Grahamj]

On Nov 29, 2007 7:44 AM, Márcio de Jesus Soares <soicram at icmc.usp.br> wrote:
> Hi list,
>
> I want to know if GAP calculates resolutions for finite groups, Indeed,
> for semi-direct product.
>
> Thanks for attention,
>
> Márcio J. Soares
>
> ----------------------------
>        São Carlos/ SP
>      Tel.(16) 3371-8045
> ----------------------------
>
>
>
> _______________________________________________
> Forum mailing list
> Forum at mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/forum
>

gap> #An integral resolution for a smallish finite group can be found as follows:
gap> G:=SymmetricGroup(4);;
gap> R:=ResolutionFiniteGroup(G,20);;
gap> #The ZG-ranks of the first 21 terms of the resolution are:
gap> List([0..20],Dimension(R));
[ 1, 3, 6, 10, 15, 21, 28, 36, 41, 45, 50, 53, 55, 58, 63, 70, 77, 83, 90,
  95, 97 ]

gap> #An integral resolution for a larger finite group G might be found using
gap> #a suitable normal subgroup N. (This applies in the case of semi-direct products.) For example:
gap> G:=DihedralGroup(512);;
gap> N:=NormalSubgroups(G)[11];;
gap> R:=ResolutionNormalSeries([G,N,Group(Identity(G))],50);;
gap> #The ZG-ranks of the first 51 terms of the resolution are:
gap> List([0..50],Dimension(R));
[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21,
  22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40,
  41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51 ]


While I'm on the Forum I'd like to mention an unrelated topic; I'm trying to develop a "MINIMAL set of CORE functions for ELEMENTARY distributed GAP computations". I'm hoping that these might (at some future stage) 
be a useful complement to the comprehensive set of ParGap functions. If you are interested, see 
http://hamilton.nuigalway.ie/Hap/www/SideLinks/About/aboutParallel.html
and
http://hamilton.nuigalway.ie/Hap/doc/chap18.html#s0ss0 

I'm new to distributed computing, so any feedback (positive or negative) would be welcome.

All the best,
Graham (Ellis)