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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Effective bounds for the maximal order of an element in the symmetric group
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by Jean-Pierre Massias, Jean-Louis Nicolas and Guy Robin PDF
Math. Comp. 53 (1989), 665-678 Request permission

Abstract:

Let $\sigma _n$ be the symmetric group of n elements and \[ g(n) = \max _{\sigma \in \sigma _n}(\text {order of $\sigma $} ).\] We give here some effective bounds for $g(n)$ and $P(g(n))$ (greatest prime divisor of $g(n)$). Theoretical proofs are in "Evaluation asymptotique de l’ordre maximum d’un élément du groupe symétrique" (Acta Arith., v. 50, 1988, pp. 221-242). The tools used here are techniques of superior highly composite numbers of Ramanujan and bounds of Rosser and Schoenfeld on the Chebyshev function $\theta (x)$.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 665-678
  • MSC: Primary 11N45; Secondary 11Y70, 20B05, 20D60
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0979940-4
  • MathSciNet review: 979940