{"paper":{"title":"Determining Fuchsian groups by their finite quotients","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GT"],"primary_cat":"math.GR","authors_text":"Alan W. Reid, Marston D.E. Conder, Martin R. Bridson","submitted_at":"2014-01-15T16:01:11Z","abstract_excerpt":"Let $\\C(\\Gamma)$ be the set of isomorphism classes of the finite groups that are homomorphic images of $\\Gamma$. We investigate the extent to which $\\C(\\Gamma)$ determines $\\Gamma$ when $\\Gamma$ is a group of geometric interest. If $\\Gamma_1$ is a lattice in ${\\rm{PSL}}(2,\\R)$ and $\\Gamma_2$ is a lattice in any connected Lie group, then $\\C(\\Gamma_1) = \\C(\\Gamma_2)$ implies that $\\Gamma_1$ is isomorphic to $\\Gamma_2$. If $F$ is a free group and $\\Gamma$ is a right-angled Artin group or a residually free group (with one extra condition), then $\\C(F)=\\C(\\Gamma)$ implies that $F\\cong\\Gamma$. If $"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.3645","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"}