Talk:Centralizer is Normal Subgroup of Normalizer

So the claim that the quotient of the normalizer by the centralizer is isomorphic to the automorphism group of G is not correct. Rather, what the N/C Theorem says is that the aforementioned quotient is isomorphic to a subgroup of the automorphism group of the subgroup H. It is those automorphisms of H which arise via conjugation by elements from G. Hence you can conclude that it contains the group of inner automorphisms of H, but there is no guarantee that the quotient is isomorphic to the automorphism group of G. Justin Benfield (talk) 13:56, 27 August 2016 (EDT)

So I took the liberty of fixing the theorem statement. It should be correct now. Justin Benfield (talk) 14:37, 27 August 2016 (EDT)

I found where the original mistake was and fixed it so as to be what it ought to have been in the first place (that is, what it has in the book cited). --prime mover (talk) 15:25, 27 August 2016 (EDT)