# Quick question about proving that either H is contained in K or K is contained in H.

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!

• 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. – jgon Dec 4 '18 at 20:09