{
  "abstract": "Let $R$ be a nonzero commutative ring with identity, $n\\geq3$, and $σ\\in GL_n(R)$. We prove that there exist nonidentity transvections $τ_1,τ_2\\in GL_n(R)$ such that $\\big[[σ,τ_1],τ_2\\big]=I_n$. Hence, Kourovka Notebook Problem 10.46 has a stronger affirmative answer over commutative rings with identity. The proof uses rank-one operators and the existence of a nonzero functional annihilating a standard basis vector and its image under $σ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17006",
  "author_total": 1,
  "authors": [
    {
      "name": "Ihechukwu Chinyere"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38n8v2sjjd9km.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17006",
  "fulltext_url": null,
  "id": "38n8v2sjjd9km",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17006",
  "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",
      "2602|Rings, Modules, and Algebras"
    ]
  ],
  "openalex": "W7213418626",
  "pdf_url": "https://arxiv.org/pdf/2609.17006",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38n8v2sjjd9km.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:22:23Z",
      "native_id": "2609.17006",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17006"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Unipotence of a double commutator with transvections",
  "title_text": "Unipotence of a double commutator with transvections",
  "type": "preprint",
  "updated_at": "2026-10-30T12:22:23Z",
  "url": "https://research.draconitic.com/paper/38n8v2sjjd9km",
  "venue": "arXiv",
  "versions": []
}