Let $G$ be a group of order $pq$, where $p,q$ are primes, $p < q$ and $q≢1$ (mod $p$); how do we prove that $G$ is cyclic ? (I have no idea)
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5This is a standard exercise in applying some Sylow theorems, e.g. here. Or for a different way here. – Nov 01 '13 at 06:04
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1@T. Bongers: Could you please give some more hints – Nov 01 '13 at 06:05
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@T.Bongers: Ah! thanks. – Nov 01 '13 at 06:08
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Hint: Is there someone who must be normal? – Ivan Di Liberti Nov 01 '13 at 06:09
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It would be better and useful for you if you can write your solution in your own words and accept it (assuming you understood the solution with help of given links).. – Nov 01 '13 at 09:44