I'm following the theorems/proofs of Contemporary Abstract Algebra by Gallian, 8th edition, and in proving Sylow's first theorem, the text assumes the following fact, which I am unsure how to prove, and was looking for tips:(adsbygoogle = window.adsbygoogle || []).push({});

Let G be a finite group and let K be a Sylow p-subgroup of G of order ##p^{k}##.

Let ##x## be an element in ##N(K)## and suppose that ##|x| = p##. Prove that ##x \in K##.

Any ideas?

I have been able to prove it for the Abelian groups (it's trivial then), but for a general finite group?

Thanks!

BiP

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# A lemma in proving Sylow's theorem

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