Exercise 1 in Dummit and Foote section 4.4 Automorphisms reads as follows:
If Aut(G) and is conjugation by g prove that = .
Deduce that Inn(G) is a normal subgroup of Aut(G).
Can anyone help me get started on this problem?
(1) I have attached Dummit and Foote section 4.4 in case readers need to view the terminology and notation used. This upload includes the text of the exercise.
(2) I am assuming that the mapping is h gh
(3) I am not sure what Dummit and Foote mean by - unless they mean the set of automorphisms that map g into g???