{"paper":{"title":"Automorphism groups of quandles and related groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Mahender Singh, Timur Nasybullov, Valeriy Bardakov","submitted_at":"2017-05-30T13:18:56Z","abstract_excerpt":"In this paper we study different questions concerning automorphisms of quandles. For a conjugation quandle $Q={\\rm Conj}(G)$ of a group $G$ we determine several subgroups of ${\\rm Aut}(Q)$ and find necessary and sufficient conditions when these subgroups coincide with the whole group ${\\rm Aut}(Q)$. In particular, we prove that ${\\rm Aut}({\\rm Conj}(G))={\\rm Z}(G)\\rtimes {\\rm Aut}(G)$ if and only if either ${\\rm Z}(G)=1$ or $G$ is one of the groups $\\mathbb{Z}_2$, $\\mathbb{Z}_2^2$ or $\\mathbb{Z}_3$. For a big list of Takasaki quandles $T(G)$ of an abelian group $G$ with $2$-torsion we prove th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.10607","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}