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If a group satisfies $x^3=1$ for all $x$, is it necessarily abelian?

I want to show that group $G$ is abelian (i.e. $ab=ba$) if $a^{3}=e, \forall a\in G.$ I am trying so much but i cant get this so please help me out!

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    I think this has been asked before. One second.2012-07-04
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    See [this](http://math.stackexchange.com/questions/147642/if-a-group-satisfies-x3-1-for-all-x-is-it-necessarily-abelian). The result is not true. Are you leaving out some hypotheses?2012-07-04
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    Perhaps you mean $a^2=e$, or $a^3=a$?2012-07-04
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    Actully, $$a^{3}=a$$ $$\Rightarrow a^{2}a=e.a$$ $$\Rightarrow a^{2}=e.$$2012-07-05

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