> < ^ Date: Mon, 06 Dec 1999 16:38:40 GMT
> ^ From: John Murray <jcmurray@eircom.net >
> ^ Subject: Affine Groups, Holomorphs

Dear Forum,
Is there a way of getting GAP to regard
a vector space as an abelian group, and
a matrix as a homomorphism of the
underlying vector space abelian group?

Also, has anyone got a construction of
Holomorph(G) where G is a finite group?

What I want is a natural way of working
with the affine group V . GL(V), where V
is a finite dimensional vector space over a
finite field. By natural, I mean describing
the group as ordered pairs (v,m), where
v is a vector and m is a nonsingular matrix,
and (v,1)^{(1,m)} = (v*m,1), where v*m is
the image of the (row) vector v under m.

Clearly this can be done using
affine:=SemidirectProduct(v,hom,gl); where
v := CyclicGroup(q)^n; and
gl := AutomorphismGroup(v); and
hom is the identity homomorphism gl->gl,
q the size of the underlying field and n is
the dimension of V. But this is not natural.

More generally I'd like a construction for
V . H, where H is a subgroup of GL(V),
or indeed H has a factor group which is
isomorphic to a subgroup of GL(V).



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