6.15. Let G act on itself by conjugation as described in the proof of Theorem 6.25. Let x € G. The conjugacy class of x is the orbit of x for this action; i.e., it is the set {gxg-¹: ge G}. (a) Prove that G is the disjoint union of its conjugacy classes. (b) Prove that G is abelian if and only if each conjugacy classes of G contains a single element. (c) Describe the conjugacy classes of the dihedral group D3.

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