{
  "abstract": "We study subindices, subfactors, and index stability in the cyclic group $\\mathbb{Z}_n$. We prove several theorems that not only confirm a conjecture and resolve some open problems about index stability of such groups, but also provide basic tools for the characterization of finite $k$-index stable groups. As a consequence, we completely characterize all 2-element index stable subsets of $\\mathbb{Z}_n$, obtain an exact closed formula for their density, and determine all $n$ for which every 2-subset is index unstable. Finally, we present some problems and a research project extending the study to 3-subsets and general $k$-subsets.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.08805",
  "author_total": 1,
  "authors": [
    {
      "name": "M. H. Hooshmand"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a23cjq8f90s1q.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.08805",
  "fulltext_url": null,
  "id": "a23cjq8f90s1q",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.08805",
  "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.CO"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7168137779",
  "pdf_url": "https://arxiv.org/pdf/2607.08805",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a23cjq8f90s1q.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2607.08805",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.08805"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "Subindices and subfactors of $\\mathbb{Z}_n$ and $k$-index stability of finite groups",
  "title_text": "Subindices and subfactors of ℤ_n and k-index stability of finite groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/a23cjq8f90s1q",
  "venue": "arXiv",
  "versions": []
}