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

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

2011-05-09

arxiv.org/abs/1105.1610v1

Acta Math. Hungar. 105 (2004), no. 3, 187--195

Mathematics

Group Theory

Scientific paper

10.1023/B:AMHU.0000049286.70907.

Define a random variable $\xi_n$ by choosing a conjugacy class $C$ of the
Sylow $p$-subgroup of $S_{p^n}$ by random, and let $\xi_n$ be the logarithm of
the order of an element in $C$. We show that $\xi_n$ has bounded variance and
mean order $\frac{\log n}{\log p}+O(1)$, which differs significantly from the
average order of elements chosen with equal probability.

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