Le plus grand facteur premier de la fonction de Landau

TL;DR

This paper investigates the largest prime divisor of the function g(n), which represents the maximum order of permutations in the symmetric group S(n), providing various estimates for this prime divisor.

Contribution

It introduces new bounds and estimates for the largest prime divisor of g(n), enhancing understanding of permutation orders in symmetric groups.

Findings

Derived several bounds for the largest prime divisor of g(n)

Provided asymptotic estimates for the prime divisor as n increases

Improved previous results on prime divisors of permutation orders

Abstract

After Landau, we define g(n) as the maximal order of a permutation of the symmetric group S(n) on n letters. We give several estimates of the largest prime divisor of g(n).