I just finished learning about Sylow theorems and I have a quick question and was wondering if someone could help me see something. In this handout I have from a section on Sylow it gives a lemma to the first theorem and it says;(adsbygoogle = window.adsbygoogle || []).push({});

Suppose p is prime and |G| = p^n then G has normal subgroups of order p^k for all k between 1 and n.

Then it says that this is obvious from Sylow 1st thm. Obvious? How? Sylow 1st thm doesnt mention anything about the subgroups being normal. I would like to understand this before moving on.

thanks

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# Sylow first thm and normal subgroups

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