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Majoration explicite de l’ordre maximum d’un élément du groupe symétrique. (Explicit upper bound of the maximal order of an element of the symmetric group). (French) Zbl 0574.10043

Let g(n) denote the largest order of an element of the symmetric group of degree n. Landau showed that log g(n)\(\sim \sqrt{n \log n}\), as \(n\to \infty\). The author gives an explicit upper bound for \(f(n)=(\log g(n))/\sqrt{n \log n}\), namely \(f(n)<1.05314\) for all \(n\geq 1\), the maximal value being attained at \(n=1 319 766\).
Reviewer: A.Hildebrand

MSC:

11N45 Asymptotic results on counting functions for algebraic and topological structures
11A25 Arithmetic functions; related numbers; inversion formulas
20B30 Symmetric groups
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References:

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