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**Bernhard** Exercise 1 in Dummit and Foote section 4.4 Automorphisms reads as follows:

If $\displaystyle \sigma$$\displaystyle \in$ Aut(G) and $\displaystyle {\phi}_g$ is conjugation by g prove that $\displaystyle \sigma$$\displaystyle {\phi}_g$$\displaystyle {\sigma}^{-1}$ = $\displaystyle {\phi}_{\sigma{(g)}$.

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 $\displaystyle {\phi}_g$ is h $\displaystyle \longrightarrow$ gh$\displaystyle g^{-1}$

(3) I am not sure what Dummit and Foote mean by $\displaystyle {\sigma{(g)}$ - unless they mean the set of automorphisms that map g into g???