Bjorn Poonen, Kaloyan Slavov
Published 2021-07-06Version 1
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 $G=S_n$. We give an application to monodromy groups.
A Chain of Normalizers in the Sylow $2$-subgroups of the symmetric group on $2^n$ letters
The Girth of Cayley graphs of Sylow 2-subgroups of symmetric groups $S_{2^n}$ on diagonal bases
Alternating and symmetric groups with Eulerian generating graph
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