# A lemma in proving Sylow's theorem

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:

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