{
  "abstract": "Given a finite group $G$ and a factorization of its order, $|G|= a_1 a_2,$ we show that a sufficient condition for there to exist subsets $A_1,\\,A_2\\subseteq G$ such that $|A_1| = a_1,$ $|A_2| = a_2,$ and $G = A_1\\,A_2,$ is that there exist a chain of subgroups $\\{e\\} = G_0 < \\dots < G_n = G$ such that $a_1$ is the product of some subfamily of the indices $|G_i:G_{i-1}|$ (and hence $a_2$ is the product of the complementary subfamily).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.08928",
  "author_total": 1,
  "authors": [
    {
      "name": "George M. Bergman"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/77c2tq264desb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.08928",
  "fulltext_url": null,
  "id": "77c2tq264desb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.08928",
  "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": "W7202171247",
  "pdf_url": "https://arxiv.org/pdf/2608.08928",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/77c2tq264desb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:57Z",
      "native_id": "2608.08928",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.08928"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "An observation on factorizations of finite groups",
  "title_text": "An observation on factorizations of finite groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:57Z",
  "url": "https://research.draconitic.com/paper/77c2tq264desb",
  "venue": "arXiv",
  "versions": []
}