Effective Bounds for the Maximal Order of an Element in the Symmetric Group

DOI10.2307/2008729zbMath0675.10028OpenAlexW4243221852MaRDI QIDQ3829621

Jean-Pierre Massias, Jean Louis Nicolas, Guy Robin

Publication date: 1989

Full work available at URL: https://doi.org/10.2307/2008729

zbMATH Keywords

symmetric grouparithmetic functionmaximal ordercomputational number theorygreatest prime divisorsuperior highly composite numbers of Ramanujan

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Asymptotic results on counting functions for algebraic and topological structures (11N45) Software, source code, etc. for problems pertaining to number theory (11-04) Symmetric groups (20B30)

Related Items (14)

Automatic sequences and curves over finite fields ⋮ Effective bounds for certain functions concerning prime numbers ⋮ The time complexity of some algorithms for generating the spectra of finite simple groups ⋮ On the maximum orders of elements of finite almost simple groups and primitive permutation groups ⋮ Affine transformations of finite vector spaces with large orders or few cycles. ⋮ On the sum of the first \(n\) prime numbers ⋮ Unnamed Item ⋮ Finite primitive permutation groups and regular cycles of their elements. ⋮ The largest prime factor of Landau's function ⋮ Landau's function for one million billions ⋮ The graph of atomic divisors and recognition of finite simple groups ⋮ AN ARITHMETIC EQUIVALENCE OF THE RIEMANN HYPOTHESIS ⋮ An inequality for non-negative matrices ⋮ Some open questions

Cites Work

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• Approximate formulas for some functions of prime numbers
• The Maximum Order of an Element of a Finite Symmetric Group
• Majoration explicite de l'ordre maximum d'un élément du groupe symétrique
• Évaluation asymptotique de l'ordre maximum d'un élément du groupe symétrique
• Estimation de la fonction de Tchebychef θ sur le k-ième nombre premier et grandes valeurs de la fonction ω(n) nombre de diviseurs premiers de n
• Majorations Explicites Pour le Nombre de Diviseurs de N
• Ordre maximal d'un élément du groupe $S_n$ des permutations et «highly composite numbers»

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