On the proportion of elements of prime order in finite symmetric groups

2022/10/27 by Cheryl E. Praeger, Praeger, Cheryl E., Enoch Suleiman +1
Mathematics · Engineering · #Finite Group Theory Research #Limits and Structures in Graph Theory #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2210.15355

Abstract

We give a short proof for an explicit upper bound on the proportion of permutations of a given prime order p, acting on a finite set of given size n, which is sharp for certain n and p. Namely, we prove that if n≡ k\pmodp with 0≤ k≤ p-1, then this proportion is at most (p⋅ k!)^-1 with equality if and only if p≤ n<2n.

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