{
  "id": "1810.10986",
  "version": "v1",
  "published": "2018-10-25T17:19:28.000Z",
  "updated": "2018-10-25T17:19:28.000Z",
  "title": "On the asymptotic behaviour of the number of Beauville and non-Beauville $p$-groups",
  "authors": [
    "Gustavo A. Fernández-Alcober",
    "Şükran Gül",
    "Matteo Vannacci"
  ],
  "categories": [
    "math.GR"
  ],
  "abstract": "We find asymptotic lower bounds for the numbers of both Beauville and non-Beauville $2$-generator finite $p$-groups of a fixed order, which turn out to coincide with the best known asymptotic lower bound for the total number of $2$-generator finite $p$-groups of the same order. This shows that both Beauville and non-Beauville groups are abundant within the family of finite $p$-groups.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-10-25T17:19:28.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "asymptotic behaviour",
      "asymptotic lower bound",
      "generator finite",
      "total number",
      "non-beauville groups"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}