Proving a set of automorphisms of a group is a group under composition Let GG be a group and let Aut(G)Aut(G) be the set of all automorphisms of GG. Prove that Aut(G)Aut(G) is a group under the operation of composition for functions. I am not too sure if I am proving Aut(G)Aut(G) itself is a group. Would this mean then that I would have to make sure it fulfills all the group requirements? If so I am not too sure how to go about it. And to prove closure, I would think I need to pick say f,g∈Aut(G)f,g∈Aut(G) then use the fact that these are automorphisms. From here, I am not too sure how to proceed.