{
  "abstract": "Let $G$ be a finite $p$-group and let $χ,ψ\\in\\operatorname{Irr}(G)$. We prove that $$\\operatorname{Van}(χ)\\subseteq\\operatorname{Van}(ψ) \\quad\\Longrightarrow\\quad χ(1)\\midψ(1),$$ where $\\operatorname{Van}(θ)=\\{g\\in G:θ(g)=0\\}$. Consequently, two irreducible characters of a finite $p$-group with the same vanishing set have the same degree. This answers a question attributed to J. Sangroniz and recorded by Hung, Moretó, and Morotti, extending the previously known case in which one character has degree $p$. The same divisibility conclusion holds for irreducible characters of finite nilpotent groups.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.03541",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhi-Lin Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e1a2k94zsmgp9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.03541",
  "fulltext_url": null,
  "id": "e1a2k94zsmgp9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.03541",
  "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": null,
  "pdf_url": "https://arxiv.org/pdf/2611.03541",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-02",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e1a2k94zsmgp9.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:14Z",
      "native_id": "2611.03541",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.03541"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Vanishing-set inclusion and character degrees in finite $p$-groups",
  "title_text": "Vanishing-set inclusion and character degrees in finite p-groups",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:28Z",
  "url": "https://research.draconitic.com/paper/e1a2k94zsmgp9",
  "venue": "arXiv",
  "versions": []
}