DirectProduct( G_1, ..., G_n )
DirectProduct
returns a group record of the direct product D of the
groups G_1, ...., G_n which need not to have a common parent
group, it is even possible to construct the direct product of an ag group
with a permutation group.
Note that the elements of the direct product may be just represented as records. But more complicate constructions, as for instance installing a new collector, may be used. The choice of method strongly depends on the type of group arguments.
Embedding( U, D, i )
Let U be a subgroup of G_<i>. Embedding
returns a homomorphism of
U into D which describes the embedding of U in D.
Projection( D, U, i )
Let U be a supergroup of G_<i>. Projection
returns a homomorphism
of D into U which describes the projection of D onto G_<i>.
gap> s4 := Group( (1,2,3,4), (1,2) ); Group( (1,2,3,4), (1,2) ) gap> S4 := AgGroup( s4 ); Group( g1, g2, g3, g4 ) gap> D := DirectProduct( s4, S4 ); Group( DirectProductElement( (1,2,3,4), IdAgWord ), DirectProductElement( (1,2), IdAgWord ), DirectProductElement( (), g1 ), DirectProductElement( (), g2 ), DirectProductElement( (), g3 ), DirectProductElement( (), g4 ) ) gap> pr := Projection( D, s4, 1 );; gap> Image( pr ); Group( (1,2,3,4), (1,2) )
GAP 3.4.4