{
  "abstract": "Amberg and Kazarin proved that a finite group is solvable if the normalizer of every cyclic subgroup of prime power order has a solvable supplement. We substantially relax this hypothesis by requiring it only for cyclic $2$-subgroups. This condition, denoted by $\\mathrm{SSN}_2$, sharply restricts the nonabelian composition factors of the group to the family $\\PSL_2(q)$, where $q\\geq7$ is a prime power satisfying $q\\equiv3\\pmod4$. Conversely, this family is precisely the nonabelian finite simple groups that satisfy $\\mathrm{SSN}_2$. Consequently, a finite group satisfying $\\mathrm{SSN}_2$ is solvable if and only if it has no section isomorphic to one of these groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14929",
  "author_total": 2,
  "authors": [
    {
      "name": "Shou Hong Qiao"
    },
    {
      "name": "Binzhou Xia"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b2ney93tstkyz.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14929",
  "fulltext_url": null,
  "id": "b2ney93tstkyz",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14929",
  "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"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7213359479",
  "pdf_url": "https://arxiv.org/pdf/2609.14929",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b2ney93tstkyz.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:29Z",
      "native_id": "2609.14929",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14929"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Solvable Supplements to Normalizers of Cyclic 2-Subgroups",
  "title_text": "Solvable Supplements to Normalizers of Cyclic 2-Subgroups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/b2ney93tstkyz",
  "venue": "arXiv",
  "versions": []
}