{
  "abstract": "We extend recent work on analogues of Grün's Lemma from skew-braces to all semiassociative Mal'cev algebras which is a broad class of algebras encompassing all expansions of groups. The direct analogue of Grün's Lemma is known to fail for skew-braces; thus, the more general result is a characterization for perfect algebras of when the upper-central series stabilizes at the second-center. The proof is an application of the description of generating sets for commutators in Mal'cev algebras.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.35396",
  "author_total": 1,
  "authors": [
    {
      "name": "Alexander Wires"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/401f8967mv4km.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.35396",
  "fulltext_url": null,
  "id": "401f8967mv4km",
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  "landing_url": "https://arxiv.org/abs/2609.35396",
  "language": null,
  "licence": "CC-BY-SA-4.0",
  "licence_label": "CC BY-SA 4.0",
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  "licence_url": "http://creativecommons.org/licenses/by-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
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      "arxiv",
      "math.RA"
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    [
      "openalex",
      "2602|Advanced Topics in Algebra"
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  "openalex": "W7214766771",
  "pdf_url": "https://arxiv.org/pdf/2609.35396",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/401f8967mv4km.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:17Z",
      "native_id": "2609.35396",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.35396"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Grün's Lemma for Semiassociative Mal'cev Algebras",
  "title_text": "Grün's Lemma for Semiassociative Mal'cev Algebras",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/401f8967mv4km",
  "venue": "arXiv",
  "versions": []
}