{
  "abstract": "We show that if $G$ is a finite solvable group such that $E = \\mathbb Q(\\{χ(g)\\, |\\, χ\\in{\\rm Irr}(G),\\ g \\in G\\})$ is an extension of degree 2 over the rationals, then $E = \\mathbb Q(\\sqrt{\\pm d})$ for a positive integer $d$ all of whose prime divisors lie in $\\{2, 3, 5\\}$. Moreover, if $G$ has a composition factor of order 7, then either $E = \\mathbb Q(\\sqrt{2})$ or $E = \\mathbb Q(\\sqrt{-3})$. This provides a partial answer to a question of G. Navarro.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.20992",
  "author_total": 2,
  "authors": [
    {
      "name": "Sara C. Debón"
    },
    {
      "name": "Joan F. Tent"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/cn1x67e9s5788.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.20992",
  "fulltext_url": null,
  "id": "cn1x67e9s5788",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.20992",
  "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": "W7222516785",
  "pdf_url": "https://arxiv.org/pdf/2610.20992",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/cn1x67e9s5788.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:54Z",
      "native_id": "2610.20992",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.20992"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Quadratic fields of values of finite solvable groups",
  "title_text": "Quadratic fields of values of finite solvable groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:54Z",
  "url": "https://research.draconitic.com/paper/cn1x67e9s5788",
  "venue": "arXiv",
  "versions": []
}