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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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