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. 


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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. 

