We define $g(n)$ to be the maximal order of an element of the symmetric group on $n$ elements. Results about the prime factorization of $g(n)$ allow a reduction of the upper bound on the largest prime divisor of $g(n)$ to $1.328\sqrt{n\log n}$.
Maximal order for divisor functions and zeros of the Riemann zeta-function
Le plus grand facteur premier de la fonction de Landau
Pair correlation of sequences $(\lbrace a_n α\rbrace)_{n \in \mathbb{N}}$ with maximal order of additive energy
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