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If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian?
I tried to prove the following. I don't know if the result is true or if I need more hypotheses. However, I don't have any counterexamples.
Prove that if $G$ is a group such that $\forall x\in G$ we have that $x^3=e$ where $e$ is the identity then $G$ is abelian.
Please if the result is true, I'd appreciate a before giving me an answer :D