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The proportion of derangements characterizes the symmetric and alternating groups

Author(s)
Poonen, Bjorn; Slavov, Kaloyan
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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.
Date issued
2022
URI
https://hdl.handle.net/1721.1/145830
Department
Massachusetts Institute of Technology. Department of Mathematics
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

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