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The maximum order of an element of a finite symmetric group. (English) Zbl 1191.11027
Summary: Let $$\mathfrak{S}_n$$ be the symmetric group of $$n$$ elements and $g(n) = \max_{\sigma \in \mathfrak{S}_n} (\text{order of}\;\sigma).$ We give here some effective bounds for $$g(n)$$ and $$P(g(n))$$ (greatest prime divisor of $$g(n))$$.

##### MSC:
 11N45 Asymptotic results on counting functions for algebraic and topological structures 20B05 General theory for finite permutation groups 20D60 Arithmetic and combinatorial problems involving abstract finite groups
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