Does Every Group of Prime Power Order Have a Subgroup of Prime Order?

[PhysicsUnderg]

Homework Statement

Let G be a group with p^k elements, where p is a prime number and k is greater than or equal to 1. Prove that G has a subgroup of order p.

The Attempt at a Solution

I attempted to prove this by showing that the conditions for a set to be subgroup form a subgroup of order p. I have become lost, however, in my proof. Any direction would be helpful. :-)

 

[micromass]

Hi PhysicsUnderg!

Take an element g of G. What is the order of g?