{
  "abstract": "We classify all non-abelian finite simple groups that possess conjugacy classes of size $3p^n$ for some prime $p$ and non-negative integer $n$. As an application, we study the structure of the normal closure $\\langle g^G\\rangle$ of an element $g$ in an arbitrary finite group $G$, provided that the conjugacy class $g^G$ has size $3p^n$. Specifically, we provide conditions for $\\langle g^{G}\\rangle$ to be solvable and completely determine its quotient modulo the solvable radical in the non-solvable case.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.41488",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Beltrán"
    },
    {
      "name": "Changguo Shao"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6rj4q0ma145jg.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.41488",
  "fulltext_url": null,
  "id": "6rj4q0ma145jg",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.41488",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.41488",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6rj4q0ma145jg.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.41488",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.41488"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On finite simple groups possessing a conjugacy class of size 3p^n",
  "title_text": "On finite simple groups possessing a conjugacy class of size 3p^n",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/6rj4q0ma145jg",
  "venue": "arXiv",
  "versions": []
}