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Congruence properties of Zariski-dense subgroups. I. (English) Zbl 0551.20029
The authors prove the following Theorem. Let G be a connected simply connected absolutely almost simple algebraic group defined over \({\mathbb{Q}}\) and let \(\Gamma\) be a finitely generated subgroup in G(\({\mathbb{Q}})\) which is Zariski-dense in G. Then for all sufficiently large prime numbers p the reduction \(\Gamma_ p\) of \(\Gamma\) coincides withe \(G_ p({\mathbb{F}}_ p)\). They give also applications of this theorem to the study of properties of p-adic and adelic closures of various subgroups in G.
Reviewer: S.I.Gel’fand

20G20 Linear algebraic groups over the reals, the complexes, the quaternions
20H05 Unimodular groups, congruence subgroups (group-theoretic aspects)
20E07 Subgroup theorems; subgroup growth
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