The proportion of derangements characterizes the symmetric and alternating groups

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.

We added an analogue for $A_n$. 8 pages

References in corpus (1)

• The exceptional locus in the Bertini irreducibility theorem for a morphism