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Show that if G is a group, H a subgroup of G with |H| = n,...

Show that if G is a group, H a subgroup of G with |H| = n, and H is the only subgroup of G of order n, then H is a normal subgroup of G.

Hint: Show that aHa-1 is a subgroup of G and is isomorphic to H for every a ∈ G.

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