Recall that an automorphism of a group G is an isomorphism p

Recall that an automorphism of a group G is an isomorphism phi : G rightarrow G of G with itself and that the collection of all automorphisms of G, with binary operation of composition, is a group, denoted Aut(G). An inner automorphism is a map of the form phi_g : G rightarrow G, phi_g (h) = ghg^-1. Show that an inner automorphism is an automorphism, that the set of all inner automorphisms is a subgroup of Aut(G) and that it is normal.

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