Let $G$ be an abelian group. Let $a, b \in G $ and let their order be $m$ and $n$ be respectively. Is it always true that order of $ab$ is $lcm(m,n)$?
What if $m$ and $n$ are coprime to each other?
Let $G$ be an abelian group. Let $a, b \in G $ and let their order be $m$ and $n$ be respectively. Is it always true that order of $ab$ is $lcm(m,n)$?
What if $m$ and $n$ are coprime to each other?