{
  "abstract": "We give negative answers to two questions of Farjoun about localizations of groups. For every odd prime $p$, we construct a finite $p$-group $G$, an infinite non-nilpotent group $H$, and a local embedding $f\\colon G\\hookrightarrow H$. The associated localization satisfies $L_f(G)\\cong H$, showing that localizations need not preserve nilpotence and that the localization map $G\\to L(G)$ need not be surjective when $G$ is a finite $p$-group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.16241",
  "author_total": 2,
  "authors": [
    {
      "name": "Sergei O. Ivanov"
    },
    {
      "name": "Georgii Kadantsev"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/18neaz497rvv4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.16241",
  "fulltext_url": null,
  "id": "18neaz497rvv4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.16241",
  "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.CT"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2610|Homotopy and Cohomology in Algebraic Topology"
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  "openalex": "W7221803787",
  "pdf_url": "https://arxiv.org/pdf/2610.16241",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-12",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/18neaz497rvv4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.16241",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.16241"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A non-nilpotent localization of a finite p-group",
  "title_text": "A non-nilpotent localization of a finite p-group",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/18neaz497rvv4",
  "venue": "arXiv",
  "versions": []
}