Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math

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

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
magidin@math.berkeley.edu

Posts: 11,123
Registered: 12/4/04
Re: name for definition in group theory
Posted: Mar 24, 2013 6:35 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

On Sunday, March 24, 2013 12:10:01 PM UTC-5, José Carlos Santos wrote:
> 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?


No, it is not necessarily true without the Axiom of Choice. Without AC, one can construct a vector space over GF(2) that is nontrivial but has trivial automorphism group. See

http://math.stackexchange.com/questions/28145/axiom-of-choice-and-automorphisms-of-vector-spaces/29469#29469

--
Arturo Magidin



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.