For a subgroup H of G and a fixed element a ∈ G,(adsbygoogle = window.adsbygoogle || []).push({});

let H^a = {x∈ G / axa^-1 ∈ H}, it's normalizer N(H) = {a∈G / H^a=H}

Show that for any subgroup H of G, N(H) is a subgroup of G.

I know that for the first one I need to show that closure holds, an identity exists, and inverses exist. But I don't even know where to start with closure!!!

Help!!!

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# Help with Normalizers

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