# The Largest Prime Dividing the Maximal Order of an Element of $S_n$

## TL;DR

This paper investigates the prime factorization of the maximal order of elements in symmetric groups, providing bounds on the largest prime divisor that improve previous estimates.

## Contribution

It introduces new bounds on the largest prime dividing the maximal order of elements in symmetric groups, refining previous results.

## Key findings

- Largest prime divisor of g(n) is bounded by 1.328√(n log n)
- Provides a reduction in the upper bound for prime divisors
- Enhances understanding of the structure of symmetric groups

## Abstract

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 $1.328\sqrt{n\log n}$.