Corpus ID: 239024462

The proportion of derangements characterizes the symmetric and alternating groups

@inproceedings{Poonen2021ThePO,
  title={The proportion of derangements characterizes the symmetric and alternating groups},
  author={Bjorn Poonen and Kaloyan Slavov},
  year={2021}
}
Let G be a subgroup of the symmetric group Sn. If the proportion of fixedpoint-free elements in G (or a coset) equals the proportion of fixed-point-free elements in Sn, then G = Sn. The analogue for An holds if n ≥ 7. We give an application to monodromy groups.