## The set of all group automorphisms of a fixed group is a group

Solution to Abstract Algebra by Dummit & Foote 3rd edition Chapter 1.6 Exercise 1.6.20 Let $G$ be a group and let $\mathsf{Aut}(G)$ be the set of all isomorphisms $G \rightarrow G$. Prove that $\mathsf{Aut}(G)$...