Dear Ron, Using the SgpDec pacakge (sgpdec.sf.net) you can construct subgroups of the wreath product (called cascade products). See Example 5 in http://arxiv.org/abs/1303.0091.
The package is still in development, so please let me know if you need help installing/using it. best wishes, Attila On Thu, Oct 24, 2013 at 12:07 PM, Sopsku <rrbu...@cox.net> wrote: > Dear Forum > > I am tryng to use GAP to "reconstruct" the group D8 as some sort of product > of its quotient group Q=D8/Center(D8) and its Center(D8). > > gap> D8:=DihedralGroup(8); # or however best defined for this > <pc group of size 8 with 3 generators> > gap> ZD8:=Center(D8); > Group([ f3 ]) > gap> Q:=D8/ZD8; > Group([ f1, f2, <identity> of ... ]) > gap> StructureDescription(Q); > "C2 x C2" > > I know it can't be direct product. I reorganized the Cayley Graph for D8 by > grouping the cosets as nodes and and looking at the lines connecting the > nodes. They cross and so a direct product will not do it. Verify this: > > gap> d:=DirectProduct(Q,ZD8); > <pc group of size 8 with 3 generators> > gap> StructureDescription(d); > "C2 x C2 x C2" > > Not a direct product. See if I can make a semidirect product > > gap> A:=AutomorphismGroup(ZD8); > <group of size 1 with 2 generators> > gap> List(A,Order); > [ 1 ] > > I don't see how to match up any orders and proceed from here. > > I would appreciate any help as how to use GAP functionality to construct > this product Thank you for any help. > Ron > > > _______________________________________________ > Forum mailing list > Forum@mail.gap-system.org > http://mail.gap-system.org/mailman/listinfo/forum _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
