Let $A(G) := \{α ∈ Aut(G) \mid ∀U ≤ G. α(U) = U\}$.
I had to prove that $A(G)$ is A subgroup of $Aut(G)$ and that it's normal in it.
Now I need to find a group $G$ such that $A(G) \neq \{id_G\}$. I though of an example but I'm not sure in it: $G = \{e,a,a^2\}$. However, I could not find any $f\in A(G)$. Any help?