(adsbygoogle = window.adsbygoogle || []).push({}); Problem. Let G be a finite group whose order is not divisible by 3. Suppose that (ab)^{3}= a^{3}b^{3}for all a, b in G. Prove that G must be abelian.

Attempt. I know that G has no subgroups of order 3, hence no elements of order 3. Thus, if (ab)^{3}= a^{3}b^{3}= e, then ab = e right? I don't know how to proceed. Any tips?

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# Homework Help: Is G Abelian?

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