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Let $G$ be group with order $6$. Prove that either $G$ and $\Bbb Z_{6}$ are isomorphic binary structure or $G$ and $S_{3}$ are isomorphic binary structure.

I know that for isomorphic binary structure, we define a function between groups and we should check homomorphism property and bijection. But I can not define a function between them. Please help me, if you have any good idea.

amWhy
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mathsstudent
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1 Answers1

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Hint: Either your group has an element of order $6$ or not. If it has, then it is isomorphic to $\mathbb{Z}_6$. Otherwise, which are the possible orders of elemets of $G$?

José Carlos Santos
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    Please start at least cursory efforts to look for duplicates of questions before you answer them. This is a rather standard question which you'd expect to have been asked on this site before, multiple times. – amWhy Dec 04 '18 at 22:48
  • @amWhy This time, I did search for a duplicate. – José Carlos Santos Dec 04 '18 at 22:50
  • Okay, I'm fine with that. I changed the title of the question so that it, like its duplicate, is more readily accessible in the future for similar questions. – amWhy Dec 04 '18 at 22:51
  • @amWhy I had never thought of that. That's a good idea. – José Carlos Santos Dec 04 '18 at 22:52