{"paper":{"title":"Inducing Super-Approximation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.GR","authors_text":"Alireza Salehi Golsefidy, Xin Zhang","submitted_at":"2018-02-10T09:53:23Z","abstract_excerpt":"Let $\\Gamma_2\\subseteq \\Gamma_1$ be finitely generated subgroups of ${\\rm GL}_{n_0}(\\mathbb{Z}[1/q_0])$. For $i=1$ or $2$, let $\\mathbb{G}_i$ be the Zariski-closure of $\\Gamma_i$ in $({\\rm GL}_{n_0})_{\\mathbb{Q}}$, $\\mathbb{G}_i^{\\circ}$ be the Zariski-connected component of $\\mathbb{G}_i$, and let $G_i$ be the closure of $\\Gamma_i$ in $\\prod_{p\\nmid q_0}{\\rm GL}_{n_0}(\\mathbb{Z}_p)$.\n  In this article we prove that, if $\\mathbb{G}_1^{\\circ}$ is the smallest closed normal subgroup of $\\mathbb{G}_1^{\\circ}$ which contains $\\mathbb{G}_2^{\\circ}$ and $\\Gamma_2\\curvearrowright G_2$ has spectral ga"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.03561","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"}