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?*
Notes:

(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???