{"paper":{"title":"On abstract commensurators of surface groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Daniel Studenmund, Khalid Bou-Rabee","submitted_at":"2018-10-29T00:11:46Z","abstract_excerpt":"Let $\\Gamma$ be the fundamental group of a surface of finite type and Comm$(\\Gamma)$ be its abstract commensurator. Then Comm$(\\Gamma)$ contains the solvable Baumslag--Solitar groups $\\langle a ,b : a b a^{-1} = b^n \\rangle$ for any $n > 1$. Moreover, the Baumslag--Solitar group $\\langle a ,b : a b^2 a^{-1} = b^3 \\rangle$ has an image in Comm$(\\Gamma)$ that is not residually finite. Our proofs are computer-assisted. Our results also illustrate that finitely-generated subgroups of Comm$(\\Gamma)$ are concrete objects amenable to computational methods. For example, we give a proof that $\\langle a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.11909","kind":"arxiv","version":3},"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"}