{
  "abstract": "Let $p$ be a prime number. When $p$ is odd, we study finite groups in which every maximal subgroup is either non-abelian simple or $p$-nilpotent, as well as those in which every maximal subgroup is either non-abelian simple or $p$-decomposable. We prove that every non-simple, non-solvable group satisfying the first condition is $p$-nilpotent, and every non-simple, non-solvable group satisfying the second condition is $p$-decomposable. In addition, we determine the possible occurrence of non-abelian simple maximal subgroups in these cases. These results provide a substantial partial answer to two questions posed by V.S. Monakhov and I.N. Tyutyanov in the Kourovka Notebook concerning the non-abelian composition factors of such groups. For non-abelian simple groups, we determine those satisfying the corresponding conditions within the alternating and sporadic families. The case of simple groups of Lie type is left open. Finally, for $p=2$, we obtain a complete classification of the non-solvable finite groups whose maximal subgroups are either non-abelian simple or $2$-nilpotent.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.06434",
  "author_total": 2,
  "authors": [
    {
      "name": "Antonio Beltrán"
    },
    {
      "name": "Fernando Viudez"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/65z7nv3j3ke0e.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.06434",
  "fulltext_url": null,
  "id": "65z7nv3j3ke0e",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.06434",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7167731114",
  "pdf_url": "https://arxiv.org/pdf/2607.06434",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/65z7nv3j3ke0e.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2607.06434",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.06434"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Finite groups with simple or $p$-nilpotent maximal subgroups",
  "title_text": "Finite groups with simple or p-nilpotent maximal subgroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/65z7nv3j3ke0e",
  "venue": "arXiv",
  "versions": []
}