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If H is a subgroup of G then N(H) is defined as { x belonging to G | xHx^-1 = H }. If P is p-Sylow subgroup of G, then prove that N(N(P)) = N(P).
You need to prove both directions.If H is a subgroup of G then N(H) is defined as { x belonging to G | xHx^-1 = H }. If P is p-Sylow subgroup of G, then prove that N(N(P)) = N(P).