1. The problem statement, all variables and given/known data An isomorphism of a group onto itself is called an automorphism. Prove that the set of all automorphisms of a group is itself a group with respect to composition. 2. Relevant equations To prove that this is a group I must show that it is closed on composition, there is an identity, and each element has an inverse, but proving something is a group isn't where the trouble lies. The trouble lies in reading the problem/understanding the terms. 3. The attempt at a solution First let's consider the thing called "automorphism". Is this a mapping? Say, the identity mapping? What exactly is the thing called "automorphism"? Second, what is the set of all automorphisms of a group? How many ways can you really list the group? Isn't there only one? I'm pretty confused about these meanings. I don't actually need help showing this is a group, I need help knowing what set looks like.