{
  "abstract": "In the Kourovka Notebook, V.\\,D.~Mazurov asked whether an automorphism $α$ of prime order $m$ of the infinite free Burnside group $G=B(m,q)$ of prime period $q$ that cyclically permutes the free generators of $G$ must have a nontrivial fixed point. In this paper, we show that for $m\\ge3$ the answer is negative for all sufficiently large prime periods $q$. Precisely, we prove that for any odd $m\\ge3$, there exists $q_m>0$ such that for every prime period $q>q_m$, the automorphism of $B(m,q)$ of order $m$ that cyclically permutes its free generators is fixed-point-free.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.33941",
  "author_total": 1,
  "authors": [
    {
      "name": "V. S. Atabekyan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1cp5qbe6a24cw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.33941",
  "fulltext_url": null,
  "id": "1cp5qbe6a24cw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.33941",
  "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": "W7214785639",
  "pdf_url": "https://arxiv.org/pdf/2609.33941",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1cp5qbe6a24cw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:57Z",
      "native_id": "2609.33941",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.33941"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Mazurov's question on fixed points of automorphisms of free Burnside groups",
  "title_text": "Mazurov's question on fixed points of automorphisms of free Burnside groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:44Z",
  "url": "https://research.draconitic.com/paper/1cp5qbe6a24cw",
  "venue": "arXiv",
  "versions": []
}