TITLE: What is the "order" of an automorphism of a group?
QUESTION [12 upvotes]: Can anyone please tell me what is the "order" of an automorphism of a group? I skim through some books but can't find the clear definition for this notion.
Thanks so much and I really appreciate if you give me some material about automorphism...

REPLY [2 votes]: There is an amazing beautiful Theorem of Horosevskii: Let $\sigma \in Aut(G)$, where $G$ is a non-trivial finite group. Then the order $|\sigma|$ of $\sigma$, is smaller than $|G|$. The proof is far from trivial and can be found in Marty Isaacs' book Finite Group Theory.