Groups - abstract algebra Let $G$ be a finite commutative group with an order of $pq$ where $gcd(p,q)=1$. If $G$ contains an element $a$ with an order of $p$, and an element $b$ with an order of $q$, show that $G$ is cyclic.
Well the only thing I know is that if the order of $G$ is prime then $G$ is cyclic
Can someone help me ?

Hint. Show that $ab$ generates $G$, i.e., that $o(ab) = pq$.
