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Mathematics of Computation

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

Author: Jon Grantham
Journal: Math. Comp. 64 (1995), 407-410
MSC: Primary 11N56; Secondary 11N05, 20B30
MathSciNet review: 1270619
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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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Article copyright: © Copyright 1995 American Mathematical Society