Dear GAP-Forum,
On Oct 4, 2011, at 10/4/11 8:57, Sandeep Murthy wrote: > is there a quick way to directly access the factors of a semidirect product > group? > I have constructed a semidirect product G = N \rtimes_\theta P According to the manual, section 47.2 (Semidirect product): Embedding(G,1) returns the embedding P->G, Embedding(G,2) that of N. The subgroups of G you want then can be obtained as Image of these maps. For example: gap> G:=SemidirectProduct(GL(3,2),GF(2)^3); <matrix group of size 1344 with 3 generators> gap> hom1:=Embedding(G,1); CompositionMapping( [ (5,7)(6,8), (2,3,5)(4,7,6) ] -> [ <an immutable 4x4 matrix over GF2>, <an immutable 4x4 matrix over GF2> ], <action isomorphism> ) gap> Pimg:=Image(hom1); <matrix group of size 168 with 2 generators> gap> Size(Pimg); 168 gap> hom2:=Embedding(G,2); MappingByFunction( ( GF(2)^3 ), <matrix group with 3 generators>, function( v ) ... end, function( a ) ... end ) gap> Nimg:=Image(hom2); <matrix group of size 8 with 3 generators> gap> Size(Nimg); 8 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
