{
  "abstract": "We prove that if M is an abelian group and X = Alex(M, phi) is a Latin Alexander quandle with id - phi in Aut(M), then Aut(X) is isomorphic to M semidirect C_Aut(M)(phi), Inn(X) is isomorphic to M semidirect and Out(X) is isomorphic to C_Aut(M)(phi)/. As a consequence, we obtain a description of the automorphism groups of direct products of the cyclic commutative medial quandles C_{2n+1} and the dihedral quandles R_{2n+1}, and we find their orders. Furthermore, we correct a result of Bardakov-Fedoseev [Algebra and Logic 63 (2024), no. 2, 111-142] on multiplication of quandles and prove that the Borodin-Neshchadim-Simonov and Markhinina-Nasybullov quandles can be constructed from conjugation, core, and generalized Alexander quandles, using the operation of multiplication of quandles. Finally, we consider the quotients of a quandle Q, namely the medialization Q^med, the commutativization Q^com, and the trivialization Q^tr. We prove that the conjugation quandle Conj(G) is medial if and only if gamma_2(G) <= Z(G); we find bounds for |Conj(G)^med| and prove that Core(G)^com is isomorphic to Core(G/<>). We describe commutative generalized Alexander quandles and, as a consequence, find the commutativization of the dihedral quandle: R_n^com is isomorphic to R_gcd(n,3).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.18676",
  "author_total": 2,
  "authors": [
    {
      "name": "Valeriy G. Bardakov"
    },
    {
      "name": "Birama Sangare"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/a6v8tj02k16zq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.18676",
  "fulltext_url": null,
  "id": "a6v8tj02k16zq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.18676",
  "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.GR"
    ],
    [
      "openalex",
      "2608|Mathematics and Applications"
    ]
  ],
  "openalex": "W7221828076",
  "pdf_url": "https://arxiv.org/pdf/2610.18676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/a6v8tj02k16zq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:20Z",
      "native_id": "2610.18676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.18676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Constructions and automorphisms of quandles",
  "title_text": "Constructions and automorphisms of quandles",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:20Z",
  "url": "https://research.draconitic.com/paper/a6v8tj02k16zq",
  "venue": "arXiv",
  "versions": []
}