{
  "abstract": "A subgroup $A$ of a finite group $G$ is \\emph{hereditarily $G$-permutable} if, for every subgroup $E$ with $A\\leq E\\leq G$ and every subgroup $B$ of $E$, some $G$-conjugate of $B$ permutes with $A$ in $E$. We give a new criterion for a finite group to be simple. A nontrivial finite group $G$ is simple if and only if it has no proper nontrivial hereditarily $G$-permutable subgroup. This proves the conjecture of Galt and Tyutyanov and answers Skiba's question in part \\textup{(b)} of Problem 17.112 in the Kourovka Notebook. Earlier work settled the conjecture for alternating groups, sporadic groups, exceptional groups of Lie type, and the groups ${\\rm PSL}_2(q)$ and ${\\rm PSU}_3(q)$. We prove the conjecture for all classical groups. The proof uses descent through parabolic subgroups and the classification of factorizations of finite simple groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12295",
  "author_total": 1,
  "authors": [
    {
      "name": "Shengmin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ert3v32fjt88.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12295",
  "fulltext_url": null,
  "id": "0ert3v32fjt88",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12295",
  "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": "W7221119327",
  "pdf_url": "https://arxiv.org/pdf/2610.12295",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-08",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ert3v32fjt88.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.12295",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12295"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A proof of the Galt--Tyutyanov conjecture on Skiba's question",
  "title_text": "A proof of the Galt--Tyutyanov conjecture on Skiba's question",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/0ert3v32fjt88",
  "venue": "arXiv",
  "versions": []
}