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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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


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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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Math. Comp. 64 (1995), 407-410
  • MSC: Primary 11N56; Secondary 11N05, 20B30
  • DOI:
  • MathSciNet review: 1270619