{
  "abstract": "We completely solve part (a) of Problem 17.112 in the Kourovka Notebook. We prove that a non-abelian finite simple group $G$ has a proper non-trivial ordinary $G$-permutable subgroup if and only if $G$ is isomorphic to ${\\rm PSL_2(q)}$ where $q\\geq4$ is a prime power and $q\\not\\equiv3\\pmod4$, ${}^2B_2(2^{2a+1})$ where $a\\geq1$, $J_1$, ${\\rm Sp}_4(4)$, or ${\\rm PSp}_4(p)$ where $p$ is prime and $p\\equiv1,13,17\\pmod{24}$. Moreover, we classify all proper non-trivial ordinary $G$-permutable subgroups of these groups. Every other non-abelian finite simple group $G$ has no proper non-trivial ordinary $G$-permutable subgroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12329",
  "author_total": 1,
  "authors": [
    {
      "name": "Shengmin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/253y1r454rfch.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12329",
  "fulltext_url": null,
  "id": "253y1r454rfch",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12329",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221156693",
  "pdf_url": "https://arxiv.org/pdf/2610.12329",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/253y1r454rfch.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12329",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12329"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Ordinary $G$-permutable subgroups of finite simple groups",
  "title_text": "Ordinary G-permutable subgroups of finite simple groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/253y1r454rfch",
  "venue": "arXiv",
  "versions": []
}