{
  "abstract": "Let $π$ be a set of primes. We extend the theory of left and right $π$-nilpotency in skew braces beyond the nilpotent type setting, and introduce the study of central $π$-nilpotency for finite skew braces. We investigate the relationships between these three notions, and a characterisation of central $π$-nilpotency in terms of chief factors is also established. This leads to the introduction of the $π$-Fitting ideal of a skew brace, for which we prove a local analogue of Fitting's theorem and provide a description in terms of centralisers of chief factors. Finally, we introduce the $π$-core of a skew brace and investigate its relationship with $π$-ideals and central $π$-nilpotency.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37042",
  "author_total": 4,
  "authors": [
    {
      "name": "L. Gong"
    },
    {
      "name": "M. Damele"
    },
    {
      "name": "V. Pérez-Calabuig"
    },
    {
      "name": "A. Rodríguez-Durà"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4xgp5smt2fqaj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37042",
  "fulltext_url": null,
  "id": "4xgp5smt2fqaj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37042",
  "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"
    ],
    [
      "openalex",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7224100049",
  "pdf_url": "https://arxiv.org/pdf/2610.37042",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4xgp5smt2fqaj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:53Z",
      "native_id": "2610.37042",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37042"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On $π$-nilpotencies of finite skew braces",
  "title_text": "On π-nilpotencies of finite skew braces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:53Z",
  "url": "https://research.draconitic.com/paper/4xgp5smt2fqaj",
  "venue": "arXiv",
  "versions": []
}