The largest prime dividing the maximal order of an element of 𝑆_{𝑛}

Abstract

We define g ( n ) 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 ) g(n) allow a reduction of the upper bound on the largest prime divisor of g ( n ) g(n) to 1.328 n log ⁡ n 1.328\sqrt {n\log n} .