P.P.S. I see why Projection(S,1) shouldn't work for an arbitrary subgroup S of a direct product, since projection is not generally a group homomorphism, and projections of S will not generally be subgroups of S. Still, we should be able to compute projections, even when S is not directly factorable, right?
On Mon, Mar 28, 2011 at 11:45 PM, William DeMeo <williamde...@gmail.com> wrote: > Dear Forum, > > This is probably a frequently asked and/or dumb question. If so, I > apologize in advance, but I couldn't find the answer in the forum > archives. > > I see how to use the Projection function to compute projections of a > product group. Is it also possible to compute projections of a > subgroup of a product group? Apparently this is not done by simply > invoking the Projection function, as the following example shows: > > G := Group([(1,2,3,4),(1,2)]);; > H := Subgroup(G, [(1,2)]); > K := Subgroup(G, [(1,2,3,4)]); > G1xG2 := DirectProduct(G, G); > emb1 := Embedding(G1xG2, 1);; > emb2 := Embedding(G1xG2, 2);; > h := List(GeneratorsOfGroup(H), i->Image(emb1,i)); > k := List(GeneratorsOfGroup(K), i->Image(emb2,i)); > HxK := Group(Concatenation(h, k),());; > > Now Projection(G1xG2,1) and Projection(G1xG2,2) work as expected, but > Projection(HxK,1) gives: > > Error, no method found! For debugging hints type ?Recovery from NoMethodFound > Error, no 1st choice method found for `Projection' on 2 arguments called from > <function>( <arguments> ) called from read-eval-loop > Entering break read-eval-print loop ... > you can 'quit;' to quit to outer loop, or > you can 'return;' to continue > > Of course, this is just a toy example -- we already know the > projections of HxK! -- but I would like to somehow compute the > projections of more general subgroups, as in > > intsub:=IntermediateSubgroups(G1xG2, HxK); > S:=intsub.subgroups[1]; > Projection(S, 1); # returns an error, as above. > > Thank you for any suggestions you can offer. > > -William > > P.S. An unrelated, less pressing question, which I've been unable to > find in the manual or forum archives: Is there is command for changing > the current working directory in GAP? > _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
