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Let G be a cyclic p-group with subgroups H and K. Prove that either H is contained in K or K is contained in H.

I am looking at Alan Wang's answer, and I am a little confused. Why is it $H\leq K$ and not $K\leq H$? Wasn't it shown that an element $x^{p^{\beta}}$ in $K$ is also in $H$? Excuse my elementary knowledge on cyclic subgroups!

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    $\begingroup$ I agree, I think it should be $K\le H$. Next time it might be easier to just leave a comment on the answer before asking a whole new question. $\endgroup$ – jgon Dec 4 '18 at 20:09

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