{
  "abstract": "We show that the $ \\mathrm{K}_1 $-functor modeled on simple reductive groups over semilocal rings is solvable if the isotropic rank is at least $ 2 $ and that the Tits index is neither $ {}^{2} \\mathsf{E}_{6, 2}^{16'} $ nor $ \\mathsf{E}_{8, 2}^{78} $. For these two Tits indices the result is already known, but assuming that the base ring contains a field. Our result implies that the elementary subgroup (or its derived subgroup) is the maximal perfect subgroup of the reductive group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25124",
  "author_total": 1,
  "authors": [
    {
      "name": "Egor Voronetsky"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6jrdyhtxh0peb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25124",
  "fulltext_url": null,
  "id": "6jrdyhtxh0peb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25124",
  "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.KT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.25124",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6jrdyhtxh0peb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.25124",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25124"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Solvability of isotropic $ \\mathrm{K}_1 $-functor over semilocal rings",
  "title_text": "Solvability of isotropic $ \\mathrm{K}_1 $-functor over semilocal rings",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/6jrdyhtxh0peb",
  "venue": "arXiv",
  "versions": []
}