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Conclude that Aut G acts on the set of conjugacy classes of G.

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Let C(a) be the conjugacy class in G containing a. Show that for a group G, if a <- G and f: G --> G is an automorphism, then b <- C(a) if and only if f(b) <- C(f(a)). Conclude that Aut G acts on the set of conjugacy classes of G.

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The expert concludes that Aut G acts on the set of conjugacy classes of G.

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Proposition. Let G be a group, a <- G, and C(a) = {gag^-1 : g <- G} be the conjugacy class of a. If f : G --> G is an ...

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