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The problem statement, all variables and given/known data

Show that for n ≥ 3, Z(S_{n}) = {e} where e is the identity element/permutation.

The attempt at a solution

It is obvious that e is in Z(S_{n}). If there is another element a ≠ e in Z(S_{n}), then... There must be some sort of contradiction and it has to do with the fact that n ≥ 3 but I can't figure it out. Any tips?

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# Center of Symmetric Group

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