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Topic: name for definition in group theory
Replies: 15   Last Post: Mar 26, 2013 11:35 AM

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Jose Carlos Santos

Posts: 4,896
Registered: 12/4/04
Re: name for definition in group theory
Posted: Mar 24, 2013 1:10 PM
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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.

Best regards,

Jose Carlos Santos

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