Possible Duplicate:
$|G|>2$ implies $G$ has non trivial automorphism
I am doing this exercise:
Find all groups $G$, with $\text{Aut}(G)=\{1\}$.
What has been clear to me is the group $G$ should be abelian group. Because we will have $G=Z(G)$ and I see that at least all $\phi_g(x)=g^{-1}xg$ are just identity. Any help is appreciated!