{
  "abstract": "Let $R_n = \\bigvee_{i=1}^{n} S^1$ be a finite connected one-dimensional CW complex with $n \\geq 2$, and let $\\mathrm{Out}(F_n)$ be the outer automorphism group of the free group $F_n$, where $π_1(R_n)\\cong F_n$. Let $p_k:\\tilde{R}_n\\rightarrow R_n$ be the standard $k$-sheeted regular cyclic cover of $R_n$ induced by a $\\mathbb{Z}_k$-action on $\\tilde{R}_n$ (which is homotopy equivalent to $R_{n_k}$, where $n_k=k(n-1)+1$) generated by a free rotation through $2π/k$ of $\\tilde{R}_n$. Let $\\mathrm{Out}_{F_{n_k}}(F_n)$ be the liftable outer automorphism group associated with a standard $k$-sheeted normal cover $p_k$. For $n\\geq3$, we show that $\\{\\mathrm{Out}_{F_{n_k}}(F_n)\\}_{k\\geq2}$ forms an infinite family of self-normalizing subgroups of $\\mathrm{Out}(F_n)$. For $n\\geq2$, these groups are maximal if and only if $k$ is prime. Furthermore, we derive explicit finite generating sets for $\\mathrm{Out}_{F_{n_k}}(F_n)$ for $k\\geq 2$ and $n\\geq 3$. Let $\\mathcal{C}$ be the infinite chain of roses, and let $q_n:\\mathcal{C}\\longrightarrow R_n$ be the standard infinite-sheeted cover induced by $\\langle τ\\rangle$, where $τ$ is the unit translation on $\\mathcal{C}$. As a final application, we obtain a finite generating set for $\\mathrm{Out}_{F_\\infty}(F_n)$ when $n\\geq 3$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.01444",
  "author_total": 3,
  "authors": [
    {
      "name": "Rohan Suresh Mahure"
    },
    {
      "name": "Priyavrat Pandey"
    },
    {
      "name": "Kashyap Rajeevsarathy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/681b6pgqajwf6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.01444",
  "fulltext_url": null,
  "id": "681b6pgqajwf6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.01444",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.01444",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/681b6pgqajwf6.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:10Z",
      "native_id": "2611.01444",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.01444"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Generating the liftable outer automorphism groups of regular cyclic covers",
  "title_text": "Generating the liftable outer automorphism groups of regular cyclic covers",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/681b6pgqajwf6",
  "venue": "arXiv",
  "versions": []
}