{
  "abstract": "For a set $\\mathcal P$ of odd primes, let $\\operatorname{CT}_{\\mathcal P}(\\mathbb{Z})$ denote the group generated by all class transpositions whose moduli have no odd prime divisors outside $\\mathcal P$. We prove that \\[ \\bigl\\langle \\operatorname{CT}_{\\mathcal P_1}(\\mathbb{Z}),\\operatorname{CT}_{\\mathcal P_2}(\\mathbb{Z}) \\bigr\\rangle = \\operatorname{CT}_{\\mathcal P_1\\cup\\mathcal P_2}(\\mathbb{Z}) \\] for any sets $\\mathcal P_1$ and $\\mathcal P_2$ of odd primes. This gives a negative answer to Question 21.75 in the Kourovka Notebook.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.04274",
  "author_total": 1,
  "authors": [
    {
      "name": "Alex Iskra"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3nhvseyx3hv4w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.04274",
  "fulltext_url": null,
  "id": "3nhvseyx3hv4w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.04274",
  "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": "W7220740222",
  "pdf_url": "https://arxiv.org/pdf/2610.04274",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3nhvseyx3hv4w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2610.04274",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.04274"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli",
  "title_text": "Groups of Class Transpositions with Prescribed Prime Divisors of the Moduli",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/3nhvseyx3hv4w",
  "venue": "arXiv",
  "versions": []
}