{
  "abstract": "Recently, Mohan et al. [Results Math. 80 (2025), No. 4, 122] answered Freiman's $3k-4$ conjecture in right-ordered groups under certain restrictions. In this paper, we take a step further by investigating the structure of nonempty subsets $S$ of a right-ordered group satisfying the small doubling condition $|S^2| = 3|S|-3$. Moreover, we provide a complete characterization of all nonempty finite subsets $S$ of the Baumslag-Solitar group $\\mathrm{BS}(1,q)$ (with $q \\in \\mathbb{Z}$ and $q \\neq -1$) for which $|S^2| = 3|S|-3$ and the identity element is the minimum of $S$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.11194",
  "author_total": 2,
  "authors": [
    {
      "name": "Mohan"
    },
    {
      "name": "Neetu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b3fsq3f4e8h8t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.11194",
  "fulltext_url": null,
  "id": "b3fsq3f4e8h8t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.11194",
  "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.NT"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7168290679",
  "pdf_url": "https://arxiv.org/pdf/2607.11194",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b3fsq3f4e8h8t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:10Z",
      "native_id": "2607.11194",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.11194"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II",
  "title_text": "On Small Doubling in Right-Ordered Groups and Baumslag-Solitar Groups-II",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:10Z",
  "url": "https://research.draconitic.com/paper/b3fsq3f4e8h8t",
  "venue": "arXiv",
  "versions": []
}