{
  "id": "2405.13603",
  "version": "v1",
  "published": "2024-05-22T12:55:06.000Z",
  "updated": "2024-05-22T12:55:06.000Z",
  "title": "On the number of generators of groups acting arc-transitively on graphs",
  "authors": [
    "Marco Barbieri",
    "Pablo Spiga"
  ],
  "categories": [
    "math.GR",
    "math.CO"
  ],
  "abstract": "Given a finite connected graph ${\\Gamma}$ and a group $G$ acting transitively on the vertices of ${\\Gamma}$, we prove that the number of vertices of ${\\Gamma}$ and the cardinality of $G$ are bounded above by a function depending only on the cardinality of ${\\Gamma}$ and on the exponent of $G$. We also prove that the number of generators of a group $G$ acting transitively on the arcs of a finite graph ${\\Gamma}$ cannot be bounded by a function of the valency alone.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-22T12:55:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "20B25",
      "05C25"
    ],
    "keywords": [
      "groups acting",
      "generators",
      "cardinality",
      "finite graph"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}