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

If H ≤ G is cyclic and normal in G, prove that every subgroup of H is also normal in G.

The attempt at a solution

Let H = <h>. We know that for g in G, h^{i}= gh^{j}g^{-1}by the normality of H. A simple induction shows that h^{in}= gh^{jn}g^{-1}, so that <h^{i}> = g<h^{j}>g^{-1}. Now all I need to show is that h^{j}belongs to <h^{i}>. I'm having trouble with this. Any tips?

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# Homework Help: Subgroups of a Cyclic Normal Subgroup Are Normal

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