
Re: name for definition in group theory
Posted:
Mar 24, 2013 7:26 PM


On 24/03/2013 22:35, Arturo Magidin 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 nontrivial 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/axiomofchoiceandautomorphismsofvectorspaces/29469#29469
Thanks!
Best regards,
Jose Carlos Santos

