First Sylow Theorem/Corollary

Corollary to First Sylow Theorem
Let $p$ be a prime number.

Let $G$ be a group.

Let:
 * $p^n \divides \order G$

where:
 * $\order G$ denotes the order of $G$
 * $n$ is a positive integer.

Then $G$ has at least one subgroup of order $p$.

Proof 2
This result can also be proved directly: