{
  "abstract": "A quandle is an algebraic system that can be regarded as a generalization of the conjugation operation in groups. We study a quandle construction associated with group actions and determine its structural properties, including its inner automorphism group, connected components, and subquandles. As a principal application, we establish a Cayley-type embedding theorem for finite quandles. Applying the construction to the natural action of the symmetric group, we obtain, for each $n$, a single quandle into which every quandle of cardinality $n$ embeds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.17438",
  "author_total": 1,
  "authors": [
    {
      "name": "Ryoya Kai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/31a6vr9tj8d6s.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.17438",
  "fulltext_url": null,
  "id": "31a6vr9tj8d6s",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.17438",
  "language": null,
  "licence": "CC-BY-NC-SA-4.0",
  "licence_label": "CC BY-NC-SA 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-sa/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.GT"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7213422776",
  "pdf_url": "https://arxiv.org/pdf/2609.17438",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/31a6vr9tj8d6s.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:43Z",
      "native_id": "2609.17438",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.17438"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Quandles from group actions and a Cayley-type embedding theorem",
  "title_text": "Quandles from group actions and a Cayley-type embedding theorem",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:43Z",
  "url": "https://research.draconitic.com/paper/31a6vr9tj8d6s",
  "venue": "arXiv",
  "versions": []
}