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Question as in title: I have attempted this question by saying that the homomorpism that maps G to $Z_2$ is onto, $Z_2$ is abelian so G must be abelian.

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marked as duplicate by Rob Arthan, N. F. Taussig, Henno Brandsma, Nicky Hekster group-theory May 12 '18 at 13:45

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

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    $\begingroup$ This question has been asked multiple times on this site (so go and look for the answer) and you do not have to assume that $|G|$ is a power of $2$. $\endgroup$ – Nicky Hekster May 12 '18 at 13:33
  • $\begingroup$ Apologies I will remove the question $\endgroup$ – user438263 Oct 15 '18 at 17:19
  • $\begingroup$ Removing the question is not necessary. Just next time take a closer look on this site. $\endgroup$ – Nicky Hekster Oct 15 '18 at 18:19
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We have, for all $a,b\in G$, $$abba=e=baba$$ Hence $ab=ba$

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