{
  "abstract": "We prove in this paper some analogues of the well-known group-theoretical Grün's lemma, stating that in a perfect group the first and the second centre coincide, and Baer's theorem, stating that if the quotient by the $n$th centre of a group is finite, then so is the $(n+1)$th term of the lower central series, in the scope of infinite skew left braces. These results represent significant improvements over previous work. The trifactorised group associated with a skew left brace will be crucial for our proofs.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.26286",
  "author_total": 4,
  "authors": [
    {
      "name": "A. Ballester-Bolinches"
    },
    {
      "name": "R. Esteban-Romero"
    },
    {
      "name": "L. A. Kurdachenko"
    },
    {
      "name": "P. Pérez-Altarriba"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/204m9mqk8j5qp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.26286",
  "fulltext_url": null,
  "id": "204m9mqk8j5qp",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.26286",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.RA"
    ],
    [
      "openalex",
      "2602|Advanced Topics in Algebra"
    ]
  ],
  "openalex": "W7166076513",
  "pdf_url": "https://arxiv.org/pdf/2606.26286",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/204m9mqk8j5qp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2606.26286",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.26286"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Analogues of Grün's lemma and Baer's theorem for skew left braces",
  "title_text": "Analogues of Grün's lemma and Baer's theorem for skew left braces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/204m9mqk8j5qp",
  "venue": "arXiv",
  "versions": []
}