{
  "abstract": "We give a negative answer to Problem 17.39 of the Kourovka Notebook. For every odd prime power $q$ and every $m\\geq1$, we construct a finite metabelian group $G_{m,q}$ with $Z_\\infty(G_{m,q})=1$ and $|Φ(G_{m,q})|=q$ for which the least number of system normalizers with trivial intersection is $m+1$. Thus the number is unbounded even when the order of the Frattini subgroup is fixed.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.22764",
  "author_total": 4,
  "authors": [
    {
      "name": "Ting Gong"
    },
    {
      "name": "Yuan Lu"
    },
    {
      "name": "Yong Yang"
    },
    {
      "name": "Michael Ruofan Zeng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8n9jkn60re4ny.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.22764",
  "fulltext_url": null,
  "id": "8n9jkn60re4ny",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.22764",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7214012929",
  "pdf_url": "https://arxiv.org/pdf/2609.22764",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8n9jkn60re4ny.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:27Z",
      "native_id": "2609.22764",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.22764"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Intersections of System Normalizers",
  "title_text": "On Intersections of System Normalizers",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:27Z",
  "url": "https://research.draconitic.com/paper/8n9jkn60re4ny",
  "venue": "arXiv",
  "versions": []
}