I have seen this question in I.N.Herstein, that if G>2 then G has a nontrivial automorphism.
The converse seems to be true. How to answer this question: That is G has a nontrivial automorphism, then prove that G>2.
I have seen this question in I.N.Herstein, that if G>2 then G has a nontrivial automorphism. The converse seems to be true. How to answer this question: That is G has a nontrivial automorphism, then prove that G>2. 

closed as too localized by Anton Geraschenko Nov 4 '09 at 21:35This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center. If this question can be reworded to fit the rules in the help center, please edit the question. 


Which direction are you asking for a proof for? The converse is very easy, as one only has to show that Z/2 (the only group of order 2) has no nontrivial automorphisms. This is obvious. It's not too hard to prove the other direction either, but I can't tell whether you're interested in that or not. 

