{
  "id": "2405.14287",
  "version": "v1",
  "published": "2024-05-23T08:02:41.000Z",
  "updated": "2024-05-23T08:02:41.000Z",
  "title": "Maps, simple groups, and arc-transitive graphs",
  "authors": [
    "Martin W. Liebeck",
    "Cheryl E. Praeger"
  ],
  "comment": "48 pages (including 6 pages of results tables at the end)",
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "We determine all factorisations $X=AB$, where $X$ is a finite almost simple group and $A,B$ are core-free subgroups such that $A\\cap B$ is cyclic or dihedral. As a main application, we classify the graphs $\\Gamma$ admitting an almost simple arc-transitive group $X$ of automorphisms, such that $\\Gamma$ has a 2-cell embedding as a map on a closed surface admitting a core-free arc-transitive subgroup $G$ of $X$. We prove that apart from the case where $X$ and $G$ have socles $A_n$ and $A_{n-1}$ respectively, the only such graphs are the complete graphs $K_n$ with $n$ a prime power, the Johnson graphs $J(n,2)$ with $n-1$ a prime power, and 14 further graphs. In the exceptional case, we construct infinitely many graph embeddings.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-23T08:02:41.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "20D06",
      "20D08",
      "05C25"
    ],
    "keywords": [
      "simple group",
      "arc-transitive graphs",
      "prime power",
      "core-free subgroups",
      "johnson graphs"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 48,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}