Dear GAP-forum, Dear Kursat Aker,
> Gi := Dihedral(8); > n := 3;S_n := SymmetricGroup( n ); > G := WreathProduct( Gi, S_n ); > x := One(G); > x![1] := 3; This access to internal components, while not technically prohibited, is not advisable. - The internal structures are not documented and not guaranteed to stay fixed between versions - doing so is very representation dependent. If you use instead DihedralGroup(IsPermGroup,8) this kind of access will not work. - Finally, modifying internal components of objects is likely to lead to the system to become seriously confused. > > I don't know what ! means. Does this allow me to change an immutable object > such > as One(G) ? Yes -- this access is apparently possible for these particular objects, but the existing code assumes that nothing like this would happen. Basically after such an assignment the group created is broken. > Question (2): > ------------- > > How can I create elements inside the wreath product ? The proper way to create elements (independent of the representation) is to use homomorphisms: E.g. for elements a,b,c in D8 and d in Sn create the element (a,b,c;d) in the wreath product use: emb:=List([1..4],x->Embedding(G,x));; Image(emb[1],a)*Image(emb[2],b)*Image(emb[3],c)*Image(emb[4],d); You can similarly use these homomorphisms (and the one returned by Projection(G)) to decompose, using PreImagesRepresentative (after dividing off the S3-part). Regards, 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 _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
