> < ^ Date: Mon, 13 Oct 1997 15:54:07 +1000
> < ^ From: Burkhard Hoefling <b.hoefling@tu-bs.de >
< ^ Subject: Re: Semidirect Product

Dear Forum,

I am sorry to say that my answer to message from Bruce Colletti
SemidirectProduct was partially wrong, which I only discovered after Bruce
contacted me again. Please take my apologies for any confusion I may have

The homomorphism a is, of course, not one from G to H, but from G to a
group A operating on H.

However, the point is that "operation", "operates" means that every element
x of A (viz. of the image of a in A) is an automorphism on H, which is
given by h -> h^x. Here, it is assumed (without verification) that the map
h -> h^x is, indeed, an automorphism of H.

In Bruce's case, this is definitely not the case, since (1,2)^(1,2,3) =3D
(2,3) is not contained in the subgroup H =3D <(1,2)>.

Sorry for any inconvenience.

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