{
  "id": "2404.18753",
  "version": "v1",
  "published": "2024-04-29T14:51:30.000Z",
  "updated": "2024-04-29T14:51:30.000Z",
  "title": "Fixers and derangements of finite permutation groups",
  "authors": [
    "Hong Yi Huang",
    "Cai Heng Li",
    "Yi Lin Xie"
  ],
  "comment": "40 pages",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-04-29T14:51:30.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "finite permutation groups",
      "simple primitive groups",
      "derangements",
      "finite transitive permutation group",
      "special case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 40,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}