Let G be a group, let H < G, and let x E G. We use the notation xHx1 to denote the set of elements {xhx1h E H}. (xHx is called a conjugate of H.) Prove that xHx-1 is a subgroup of G (a) If H is finite, then how are |H| and |xHx (b) (c) related? Prove that H is isomorphic to xHx1

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