Perfect. Thank you! -wjd On Tue, Mar 29, 2011 at 2:27 PM, Alexander Hulpke <ahul...@gmail.com> wrote: > Dear forum, Dear William, > >> >> 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 > > Projection returns a stored projection function of a direct or semidirect > product. It thus applies only to the full product. > However, as it is a homomorphism, it of course can be applied to any subgroup > of the product, so you could take for example > > proj:=Projection(G1xG2,1); > Image(proj,HxK); > > If you want to restrict the projection to the subgroup (primarily of > relevance for computing pre-images) you could use > > rest:=RestrictedMapping(proj,HxK); > >> 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. > > Again here I would simply use the same projection `proj' as long as it comes > to computing images, or use the restricted mapping. > >> 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? > In the IO package there is IO_chdir if you are working under Unix. > > Best, > > Alexander (Hulpke) > > -- Colorado State University, Department of Mathematics, > Weber Building, 1874 Campus Delivery, Fort Collins, CO 80523-1874, USA > email: hul...@math.colostate.edu, Phone: ++1-970-4914288 > http://www.math.colostate.edu/~hulpke > > > >
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