Miller, William The maximum order of an element of a finite symmetric group. (English) Zbl 1191.11027 Am. Math. Mon. 94, No. 6, 497-506 (1987). 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 \(g(n))\). Cited in 23 Documents 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 PDFBibTeX XMLCite \textit{W. Miller}, Am. Math. Mon. 94, 497--506 (1987; Zbl 1191.11027) Full Text: DOI Link