[GAP Forum] Semidirect products

[Alexander Hulpke]

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,
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