5. Let G be a group and let H be a subgroup of G. For each g e G, we define the subset gHg-1 of G by 9H9¬ = {ghg¬ |he H}. -1 Assume that |G| < 00. Prove that H is normal in G A gHq-1 = H for every g E G. (Hint for () : Show that for each g E G the map g: H → H, 9(h) = ghg-1 is well defined and bijective.)

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