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

C.E. Praeger; E. Suleiman

doi:10.48550/arXiv.2210.15355

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

C.E. Praeger, E. Suleiman

School of Physics, Mathematics and Computing

Research output: Working paper › Preprint

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 set of given size n, which is sharp for certain n and p. Namely, we prove that if n ≡ k (mod p) with 0 ≤ k ≤ p−1, then this proportion is at most (p · k!)−1 with equality if and only if p ≤ n < 2n.

Original language	English
Publisher	arXiv
Pages	251-256
Number of pages	6
DOIs	https://doi.org/10.48550/arXiv.2210.15355
Publication status	Published - 27 Oct 2022

Publication series

Name	International Journal of Group Theory
Publisher	University of Isfahan
ISSN (Print)	2251-7650

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10.48550/arXiv.2210.15355

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

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

Abstract

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ON THE PROPORTION OF ELEMENTS OF PRIME ORDER IN FINITE SYMMETRIC GROUPS

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