{
  "abstract": "We resolve the remaining cases of a longstanding problem on the lower and upper Lie nilpotency indices of modular group algebras. Equality of the two indices has been known in characteristics greater than three since 1992; we establish it in the remaining characteristics two and three, thereby completing the problem for finite groups of prime-power order over finite fields. The proof gives a uniform argument for every prime and introduces a terminal restricted Poincare-Birkhoff-Witt construction that converts the lower-Lie problem into a chronological reachability argument, with no structural hypothesis on the derived subgroup.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10915",
  "author_total": 1,
  "authors": [
    {
      "name": "Joe Gildea"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bzrjqvgphp7e0.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10915",
  "fulltext_url": null,
  "id": "bzrjqvgphp7e0",
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  "landing_url": "https://arxiv.org/abs/2610.10915",
  "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.RA"
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    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7221114034",
  "pdf_url": "https://arxiv.org/pdf/2610.10915",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bzrjqvgphp7e0.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:58Z",
      "native_id": "2610.10915",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10915"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RA",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Lower and Upper Lie Nilpotency Indices of Modular Group Algebras",
  "title_text": "Lower and Upper Lie Nilpotency Indices of Modular Group Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:58Z",
  "url": "https://research.draconitic.com/paper/bzrjqvgphp7e0",
  "venue": "arXiv",
  "versions": []
}