Date: Mar 24, 2013 1:10 PM
Author: Jose Carlos Santos
Subject: Re: name for definition in group theory
On 24-03-2013 16:44, David C. Ullrich wrote:
> Since G is abelian, the map x -> -x is an automorphism.
> Since this must be trivial, we have x + x = 0 for all
> x. Hence G is a vector space over Z_2. And now as
> above, if dim(G) = 0 or 1 then |G| = 1 or 2, while
> if dim(G) > 1 then G has a non-trivial automorphism.
Is this necessarily true without the axiom of choice? With it, yes, it
is true: you just take a base of G over Z_2 and then you use it to get a
non-trivial automorphism. But without the axiom of choice, I don't see
why is it still possible to get such an automorphism.
Jose Carlos Santos