On Nov 29, 2007 7:44 AM, Márcio de Jesus Soares <[EMAIL PROTECTED]> 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 > [email protected] > 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) _______________________________________________ Forum mailing list [email protected] http://mail.gap-system.org/mailman/listinfo/forum
