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

Not what you're looking for? Search our solutions OR ask your own Custom question.

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.

Â© BrainMass Inc. brainmass.com March 4, 2021, 11:41 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/conclude-aut-g-acts-set-conjugacy-classes-g-446618

#### Solution Preview

I have used LaTeX to generate the attached PDF file. Please refer to the attachment for clear notations.

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 ...

#### Solution Summary

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

$2.49