Fixers and derangements of finite permutation groups
- Resource Type
- Working Paper
- Authors
- Huang, Hong Yi; Li, Cai Heng; Xie, Yi Lin
- Source
- Subject
- Mathematics - Group Theory
Mathematics - Combinatorics
- Language
Let $G\leqslant\mathrm{Sym}(\Omega)$ be a finite transitive permutation group with point stabiliser $H$. We say that a subgroup $K$ of $G$ is a fixer if every element of $K$ has fixed points, and we say that $K$ is large if $|K| \geqslant |H|$. There is a special interest in studying large fixers due to connections with Erd\H{o}s-Ko-Rado type problems. In this paper, we classify up to conjugacy the large fixers of the almost simple primitive groups with socle $\mathrm{PSL}_2(q)$, and we use this result to verify a special case of a conjecture of Spiga on permutation characters. We also present some results on large fixers of almost simple primitive groups with socle an alternating or sporadic group.
Comment: 33 pages