{
  "abstract": "For a finite group $G$, let $ρ^{*}(G)$ be the set of primes dividing some sub-class size of $G$, and let $σ^{*}(G)$ be the maximum number of distinct prime divisors of a sub-class size. Motivated by the conjugacy-class version of Huppert's $ρ$--$σ$ problem, we prove that \\[ |ρ^{*}(G)|<2σ^{*}(G) \\] for every finite nonnilpotent group $G$. This answers \\cite[Remark~5.3]{QY} and extends to arbitrary finite nonnilpotent groups the coefficient-$2$ bound proved in \\cite[Theorem~1.7]{QY} for solvable nonnilpotent groups. The coefficient $2$ is best possible. The proof does not use the classification of finite simple groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.29662",
  "author_total": 1,
  "authors": [
    {
      "name": "Yong Yang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/eyzb1ma5mwp8g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.29662",
  "fulltext_url": null,
  "id": "eyzb1ma5mwp8g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.29662",
  "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": "W7214288727",
  "pdf_url": "https://arxiv.org/pdf/2609.29662",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/eyzb1ma5mwp8g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:15Z",
      "native_id": "2609.29662",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.29662"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "A Huppert-type $ρ^*$--$σ^*$ theorem for sub-class sizes",
  "title_text": "A Huppert-type ρ^*--σ^* theorem for sub-class sizes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:15Z",
  "url": "https://research.draconitic.com/paper/eyzb1ma5mwp8g",
  "venue": "arXiv",
  "versions": []
}