Assume two natural numbers $m,n$ are coprime such that $a^m b^m=b^m a^m$ and $a^n b^n=b^n a^n$. Then $G$ is an abelian group
A group such that $a^m b^m = b^m a^m$ and $a^n b^n = b^n a^n$ ($m$, $n$ coprime) is abelian?