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

Grantham, Jon

doi:10.1090/S0025-5718-1995-1270619-3

The largest prime dividing the maximal order of an element of $S_ n$
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Math. Comp. 64 (1995), 407-410 Request permission

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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Über die Maximalordnung der Permutationen gegebenen Grades

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