On the proportion of elements of prime order in finite symmetric groups
Year: 2022
Type: article
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 $n\equiv k\pmod{p}$ with $0\leq k\leq p-1$, then this proportion is at most $(p\cdot k!)^{-1}$ with equality if and only if $p\leq n<2n$.
Authors: Praeger, Cheryl E., Suleiman, Enoch
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7111331218