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arXiv · 1903.06817

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

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

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Jon Grantham. 2019-03-15. The Largest Prime Dividing the Maximal Order of an Element of $S_n$. https://doi.org/10.1090/s0025-5718-1995-1270619-3

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