Hi guys,

I've been asked to prove the following:

Prove that every group whose order is a power of a prime $\displaystyle p$ contains an element of order $\displaystyle p$.

This is the proof I've come up with. I feel like it is really long and contrived. The only tools that I have at my disposal is LaGrange's Theorem and the associated corollaries.

Uploaded with ImageShack.us