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)

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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?

Peter