{"paper":{"title":"Commutation Semigroups of Finite Metacyclic Groups with Trivial Centre","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.RA","authors_text":"Charles C. Edmunds, Darien DeWolf","submitted_at":"2018-07-26T22:36:13Z","abstract_excerpt":"We study the right and left commutation semigroups of finite metacyclic groups with trivial centre. These are presented \\[G(m,n,k) = \\left\\langle {a,b;{a^m} = 1,{b^n} = 1,{a^b} = {a^k}} \\right\\rangle \\quad (m,n,k\\in\\mathbb{Z}^+)\\] with $(m,k - 1) = 1$ and $n = in{d_m}(k),$ the smallest positive integer for which ${k^n} = 1\\,\\pmod m,$ with the conjugate of $a$ by $b$ written ${a^b}( = {b^{ - 1}}ab).$ The \\emph{right} and \\emph{left commutation semigroups of} $G,$ denoted ${\\rm P}(G)$ and $\\Lambda (G),$ are the semigroups of mappings generated by $\\rho (g):G \\to G$ and $\\lambda (g):G \\to G$ defi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.10389","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"}