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Prove that any group of order 561 is cyclic.

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As you are a new user I would like to tell you that : It would not be enough to just write the question to get a reply... please explain what you have tried? –  Praphulla Koushik Dec 13 '13 at 7:17
    
15 not prim but is cyclic. –  ayoob Dec 13 '13 at 7:20
    
@Magdiragdag : fine fine :) –  Praphulla Koushik Dec 13 '13 at 7:23
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@ayoob: At least you should describe your background, what did you learn and what difficulties did you encountered so that you know what hints and answers should be given. –  John Dec 13 '13 at 7:27
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N(H)/C(H) -----> AUT(H) normalizer - central theorem –  ayoob Dec 13 '13 at 7:31

1 Answer 1

In general, there is only one group of order $n$ iff gcd$(n,\varphi(n))=1$. Of course such a group must be necessarily cyclic. 561 satisfies the condition.

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Isn't this more advanced for a beginner? –  Praphulla Koushik Dec 13 '13 at 8:43
    
????????????????????????? –  ayoob Dec 13 '13 at 9:44
    
i cofused about this –  ayoob Dec 13 '13 at 9:45
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@NickyHekster This is really a neat fact. I had never heard of it either, until now. –  rschwieb Dec 18 '13 at 16:05
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@rschwieb Yes, I think so too! And the nice thing of it it is so simple and you will never forget it! –  Nicky Hekster Dec 18 '13 at 16:26

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