{"paper":{"title":"On fully residually-$\\mathcal{R}$ groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Inna Bumagin, Ming Ming Zhang","submitted_at":"2018-01-13T18:46:03Z","abstract_excerpt":"We consider the class $\\mathcal{R}$ of finitely generated toral relatively hyperbolic groups. We show that groups from $\\mathcal{R}$ are commutative transitive and generalize a theorem proved by Benjamin Baumslag to this class. We also discuss two definitions of (fully) residually-$\\mathcal{C}$ groups and prove the equivalence of the two definitions for $\\mathcal{C}=\\mathcal{R}$. This is a generalization of the similar result obtained by Ol'shanskii for $\\mathcal{C}$ being the class of torsion-free hyperbolic groups. Let $\\Gamma\\in\\mathcal{R}$ be non-abelian and non-elementary. We prove that e"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.04475","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"}