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    Normalizer of a Subgroup of a Group

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    Modern Algebra
    Group Theory (XLVI)
    Normal Subgroups of a Group
    Normalizer of a Subgroup of a Group
    Centralizer of a Subgroup of a Group

    If H is a subgroup of G, let N(H) = {g belongs to G|gHg^-1 = H}. Prove that H is normal in N(H).

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    Solution Summary

    It is proven that H is normal in N(H), where H is a subgroup of G and N(H) = {g belongs to G|gHg^-1 = H}.
    The solution is detailed and well presented.

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