The proportion of derangements characterizes the symmetric and alternating groups
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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
2022Department
Massachusetts Institute of Technology. Department of MathematicsJournal
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