Dummit and Foote Section 4.4 Automorphisms Exercise 1 reads as follows:
Let and is conjugation by g, prove that = .
Deduce that Inn(G) is a normal subgroup of Aut(G)
A start to the proof is as follows:
Thus = .
My question is - how do we use this result to show Inn(G) is a normal subgroup of Aut(G)?
Can someone please help?