{"paper":{"title":"On groups elementarily equivalent to a group of triangular matrices $T_n(R)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.LO"],"primary_cat":"math.GR","authors_text":"Alexei Miasnikov, Mahmood Sohrabi","submitted_at":"2016-09-30T16:32:43Z","abstract_excerpt":"In this paper we investigate the structure of groups elementarily equivalent to the group $T_n(R)$ of all invertible upper triangular $n\\times n$ matrices, where $n\\geq 3$ and $R$ is a characteristic zero integral domain. In particular we give both necessary and sufficient conditions for a group being elementarily equivalent to $T_n(R)$ where $R$ is a characteristic zero algebraically closed field, a real closed field, a number field, or the ring of integers of a number field."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09802","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"}