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

Praeger, Cheryl E.; Suleiman, Enoch

doi:10.22108/ijgt.2023.135509.1810

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	On the proportion of elements of prime order in finite symmetric groups
International Journal of Group Theory
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 19 فروردین 1402 اصل مقاله (405.29 K)
نوع مقاله: 2022 CCGTA IN SOUTH FLA
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.135509.1810
نویسندگان
Cheryl E. Praeger^* ¹؛ Enoch Suleiman²
¹Centre for the Mathematics of Symmetry and Computation, University of Western Australia, 35 Stirling Highway, Perth 6009, Australia
²Department of Mathematics, Federal University Gashua, Yobe State, Nigeria
چکیده
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 $n\equiv k\pmod{p}$ with $0\leq k\leq p-1$, then this proportion is at most $(p\cdot k!)^{-1}$ with equality if and only if $p\leq n<2n$.
کلیدواژه‌ها
Finite symmetric groups؛ element proportions؛ elements of prime order

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