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It seems that there are many ways to prove the Sylow theorems. I'd like to see a collection of them. Please write down or share links to any you know.

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    Check out the early chapters of [Dixon & Mortimer](http://books.google.fi/books/about/Permutation_Groups.html?id=4QDpFN6k61EC&redir_esc=y) for a nice selection of proofs of basic facts about group theory.2012-06-22

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