[GAP Forum] a semidirect product
Anvita *
anvita21 at usa.com
Sat Aug 14 16:38:44 BST 2004
Dear forum,
Given a group Q, how can I construct the semidirect Product (Q x Q):Aut(Q),
where Aut(Q) acts on Q x Q componentwise?
In order to use SemidirectProduct, I need to define
the right embedding Aut(Q) -> Aut(Q X Q) in GAP.
here is the beginning of my program
-------------------------
# Q is given
A:=AutomorphismGroup(Q);
QQ:=DirectProduct(Q,Q);
p1:=Projection(QQ,1);
p2:=Projection(QQ,2);
e1:=Embedding(QQ,1);
e2:=Embedding(QQ,2);
L:=List(GeneratorsOfGroup(A), a->[Composition(e1,a,p1),Composition(e2,a,p2)]);
------------------------
Now, for each pair l in L, I need to mutiply the endmorphisms l[1] and l[2]
of QQ, but I have not been able to find a suitable GAP function for this.
Section 31.5 of the manual mentions "Scalar multiplication of general mappings"
but does not say how (or whether) this scalar product is imlemented in GAP.
Any help would be very appreciated.
Anvita
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