{
  "abstract": "Let $G$ be a finite group and let $\\mathrm{P}_{\\mathcal{U}}(G)$ denote the probability that two randomly chosen elements of $G$ generate a supersoluble subgroup. We prove that if $\\mathrm{P}_{\\mathcal{U}}(G) > 16/25$ then $G$ is supersoluble, and that the bound $16/25$ is sharp, being attained by the group $G = (C_5 \\times C_5) \\rtimes Q_8$, where $Q_8$ acts faithfully and irreducibly on $C_5 \\times C_5$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08165",
  "author_total": 1,
  "authors": [
    {
      "name": "Andrea Lucchini"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2v75jfqq87thk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08165",
  "fulltext_url": null,
  "id": "2v75jfqq87thk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08165",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7167898871",
  "pdf_url": "https://arxiv.org/pdf/2607.08165",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-05",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2v75jfqq87thk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2607.08165",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08165"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Supersoluble groups and the probability of generating a supersoluble subgroup",
  "title_text": "Supersoluble groups and the probability of generating a supersoluble subgroup",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/2v75jfqq87thk",
  "venue": "arXiv",
  "versions": []
}