(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

If H is any subgroup of G and [itex]N={\cap_{a\in G} a^{-1}Ha}[/itex], prove that N is a normal subgroup of G.

3. The attempt at a solution

Is this statement true? [itex]\forall n: n \in N \implies \exists h \in H : n=a^{-1}ha[/itex]

The theorem looks intuitively true, but I don't know how to write a formal argument knowing that [itex]N={\cap_{a\in G} a^{-1}Ha}[/itex]

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# Homework Help: Prove that N is a normal subgroup

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