{"paper":{"title":"Smooth skew-morphisms of the dihedral groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Junyang Zhang, Kai Yuan, Kan Hu, Naer Wang","submitted_at":"2018-06-19T02:42:52Z","abstract_excerpt":"A skew-morphism $\\varphi$ of a finite group $A$ is a permutation on $A$ such that $\\varphi(1)=1$ and $\\varphi(xy)=\\varphi(x)\\varphi^{\\pi(x)}(y)$ for all $x,y\\in A$ where $\\pi:A\\to\\mathbb{Z}_{|\\varphi|}$ is an integer function. A skew-morphism is smooth if $\\pi(\\varphi(x))=\\pi(x)$ for all $x\\in A$. The concept of smooth skew-morphisms is a generalization of that of $t$-balanced skew-morphisms. The aim of the paper is to develop a general theory of smooth skew-morphisms. As an application we classify smooth skew-morphisms of the dihedral groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07023","kind":"arxiv","version":1},"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"}