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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).

Thanks,

John

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