{
  "abstract": "For a fixed prime $p$, a group is called a $p'$-group if the orders of all its elements are coprime to $p$. It is well known that in a finite $p'$-group an automorphism of order $p$ is regular if and only if it is a splitting automorphism of period $p$. In the Kourovka Notebook, V.\\,D.~Mazurov asked whether these two notions coincide for periodic $p'$-groups. We answer this question in the negative by constructing a periodic group of prime period $q$ that admits a regular automorphism of order $p \\neq q$ which is not splitting.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.15360",
  "author_total": 1,
  "authors": [
    {
      "name": "V. S. Atabekyn"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/f11d0e681mmmn.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.15360",
  "fulltext_url": null,
  "id": "f11d0e681mmmn",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.15360",
  "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",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7221762024",
  "pdf_url": "https://arxiv.org/pdf/2610.15360",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/f11d0e681mmmn.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.15360",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.15360"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Regular automorphisms of periodic $p'$-groups need not be splitting",
  "title_text": "Regular automorphisms of periodic p'-groups need not be splitting",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/f11d0e681mmmn",
  "venue": "arXiv",
  "versions": []
}