Conjugate subgroups. Let G be a group, let H < G, and let x € G. We use the notation xHx-1 to denote the set of elements {xhx-1 | h E H}. (xHx-1 is called a conjugate of H.) (a) Prove that xHx-1 is a subgroup of G. (b) If H is finite, then how are |H| and |¤H׬| related? (c) Prove that H is isomorphic to xHx-.

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