MathNet 2017-part-05 — 176 problems (EN–VI) Question 23

Let $G$ be a group and let $m$ and $n$ be relatively prime positive integers. Show that, if the functions $f: G \to G$, $f(x) = x^{m+1}$, and $g: G \to G$, $g(x) = x^{n+1}$, are both surjective endomorphisms, then $G$ is commutative.
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