## Group of Order $pq$ Has a Normal Sylow Subgroup and Solvable

## Problem 245

Let $p, q$ be prime numbers such that $p>q$.

If a group $G$ has order $pq$, then show the followings.

**(a)** The group $G$ has a normal Sylow $p$-subgroup.

**(b)** The group $G$ is solvable.