3. Let G be a group. Recall that if x E G, we defined the conjugacy class of x in G, denoted by class(x), to be -1 class(x) = {y Gy is conjugate to x} = {gxg¯¹ | g € G}. Show that G is partitioned by the conjugacy classes. (Hint: Let G act on X = G by conjugation. What are the orbits?)

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