The order of elements in Sylow p-subgroups of the symmetric group

Author： Schlage-Puchta Jan-Christoph  

Publisher： Springer Publishing Company

ISSN： 0236-5294

Source： Acta Mathematica Hungarica, Vol.105, Iss.3, 2004-11, pp. : 187-195

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Abstract

Define a random variable ξn by choosing a conjugacy class C of the Sylow p-subgroup of Spn by random, and let ξn be the logarithm of the order of an element in C. We show that ξn has bounded variance and mean order log n /log p +O(1), which differs greatly from the average order of elements chosen with equal probability.

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