{"paper":{"title":"On variants of the extended bicyclic semigroup","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GN"],"primary_cat":"math.GR","authors_text":"Kateryna Maksymyk, Oleg Gutik","submitted_at":"2018-05-14T03:08:33Z","abstract_excerpt":"In the paper we describe the group $\\mathbf{Aut}\\left(\\mathscr{C}_{\\mathbb{Z}}\\right)$ of automorphisms of the extended bicyclic semigroup $\\mathscr{C}_{\\mathbb{Z}}$ and study the variants $\\mathscr{C}_{\\mathbb{Z}}^{m,n}$ of the extended bicycle semigroup $\\mathscr{C}_{\\mathbb{Z}}$, where $m,n\\in\\mathbb{Z}$. In particular, we prove that $\\mathbf{Aut}\\left(\\mathscr{C}_{\\mathbb{Z}}\\right)$ is isomorphic to the additive group of integers, the extended bicyclic semigroup $\\mathscr{C}_{\\mathbb{Z}}$ and every its variant are not finitely generated, and describe the subset of idempotents $E(\\mathscr{"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.04995","kind":"arxiv","version":2},"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"}