The proportion of derangements characterizes the symmetric and alternating groups

Poonen, Bjorn; Slavov, Kaloyan

The proportion of derangements characterizes the symmetric and alternating groups

Name

Bulletin of London Math Soc - 2022 - Poonen - The proportion of derangements characterizes the symmetric and alternating.pdf

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Published version

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116.42 KB

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4572141702a2ea22752f575bf0f1be91

sword-2022-10-14T15:08:17.original.xml (130 B)

Original SWORD entry document

Author(s)

Poonen, Bjorn

•

Slavov, Kaloyan

Date Issued

2022

Journal

Bulletin of the London Mathematical Society

Publisher

Wiley

Citation

Poonen, Bjorn and Slavov, Kaloyan. 2022. "The proportion of derangements characterizes the symmetric and alternating groups." Bulletin of the London Mathematical Society, 54 (4).

Version

Final published version

Abstract

Let $G$ be a subgroup of the symmetric group $S_n$. If the proportion of fixed-point-free elements in $G$ (or a coset) equals the proportion of fixed-point-free elements in $S_n$, then $G=S_n$. The analogue for $A_n$ holds if $n \ge 7$. We give an application to monodromy groups.

MIT Department

Massachusetts Institute of Technology. Department of Mathematics

Terms of Use

Creative Commons Attribution-NonCommercial-NoDerivs License

http://creativecommons.org/licenses/by-nc-nd/4.0/

Persistent DSpace Link

https://hdl.handle.net/1721.1/145830

DOI of Published Version

https://doi.org/10.1112/BLMS.12639