Edit Profile (opens in new tab) Rapinchuk, Andrei S. Co-Author Distance Author ID: rapinchuk.andrei-s Published as: Rapinchuk, A. S.; Rapinchuk, Andrei S.; Rapinchuk, Andrei; Rapinchuk, A.; Rapincuk, A. S. more...less Documents Indexed: 104 Publications since 1978, including 3 Books and 4 Additional arXiv Preprints 2 Further Contributions Co-Authors: 41 Co-Authors with 78 Joint Publications 1,658 Co-Co-Authors all top 5 Co-Authors 27 single-authored 20 Prasad, Gopal 18 Rapinchuk, Igor A. 17 Platonov, Vladimir Petrovich 11 Chernousov, Vladimir I. 5 Benyash-Krivets, Valeriĭ Vatslavovich 5 Bondarenko, Aleksandr Adamovich 4 Faddeev, Lyudvig Dmitrievich 4 Margulis, Grigoriĭ Aleksandrovich 4 Novikov, Sergeĭ Petrovich 4 Segev, Yoav 4 Zel’manov, Efim Isaakovich 3 Adyan, Sergeĭ Ivanovich 3 Corvaja, Pietro 3 Potapchik, Alexander 3 Ren, Jinbo 3 Zannier, Umberto M. 2 Bukhshtaber, Viktor Matveevich 2 Bux, Kai-Uwe 2 Demeio, Julian Lawrence 2 Erovenko, Igor V. 2 Kozlov, Valeriĭ Vasil’evich 2 Parshin, Alekseĭ Nikolaevich 2 Rowen, Louis Halle 2 Yanchevskiĭ, Vyacheslav Ivanovich 1 Abramenko, Peter 1 Barkovich, O. A. 1 Efrat, Ido 1 Ershov, Mikhail V. 1 Funar, Louis 1 Garibaldi, Skip 1 Krashen, Daniel 1 Lifschitz, Lucy 1 Mal’tsev, Arkadiĭ Anatol’evich 1 Matzri, Eliyahu 1 Morgan, Aleksander 1 Osipov, Yuriĭ Sergeevich 1 Pierce, Richard Scott 1 Pollio, Timothy P. 1 Saltman, David J. 1 Seitz, Gary M. 1 Sury, Balasubramanian 1 Witte Morris, Dave 1 Zalesski, Alexandre Efimovich 1 Zhizhchenko, Alexey B. all top 5 Serials 7 Doklady Akademii Nauk BSSR 7 Soviet Mathematics. Doklady 5 Russian Mathematical Surveys 5 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Manuscripta Mathematica 4 Mathematics of the USSR. Izvestiya 4 Proceedings of the American Mathematical Society 3 Journal of Algebra 3 Journal of Number Theory 3 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 3 Mathematical Research Letters 3 Proceedings of the Steklov Institute of Mathematics 2 Israel Journal of Mathematics 2 Advances in Mathematics 2 Publications Mathématiques 2 Inventiones Mathematicae 2 IMRN. International Mathematics Research Notices 2 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 2 Algebra & Number Theory 1 Commentarii Mathematici Helvetici 1 Compositio Mathematica 1 Geometriae Dedicata 1 Journal of Soviet Mathematics 1 Mathematische Zeitschrift 1 Siberian Mathematical Journal 1 Transactions of the American Mathematical Society 1 Transactions of the Moscow Mathematical Society 1 Journal of the American Mathematical Society 1 Doklady Akademii Nauk Belarusi 1 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 1 Comptes Rendus de l’Académie des Sciences. Série I 1 Notices of the American Mathematical Society 1 Russian Academy of Sciences. Izvestiya. Mathematics 1 Russian Academy of Sciences. Doklady. Mathematics 1 Geometry & Topology 1 Chebyshevskiĭ Sbornik 1 Cambridge Studies in Advanced Mathematics 1 Pure and Applied Mathematics (Academic Press) 1 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 1 Translations. Series 2. American Mathematical Society 1 Groups, Geometry, and Dynamics 1 Bulletin of Mathematical Sciences 1 Research in the Mathematical Sciences all top 5 Fields 81 Group theory and generalizations (20-XX) 51 Number theory (11-XX) 24 Associative rings and algebras (16-XX) 22 Algebraic geometry (14-XX) 16 Topological groups, Lie groups (22-XX) 12 Field theory and polynomials (12-XX) 6 \(K\)-theory (19-XX) 5 History and biography (01-XX) 4 Combinatorics (05-XX) 4 Differential geometry (53-XX) 1 General and overarching topics; collections (00-XX) 1 Several complex variables and analytic spaces (32-XX) 1 Algebraic topology (55-XX) 1 Manifolds and cell complexes (57-XX) 1 Global analysis, analysis on manifolds (58-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 81 Publications have been cited 1,176 times in 812 Documents Cited by ▼ Year ▼ Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046 Platonov, Vladimir; Rapinchuk, Andrei 368 1994 Algebraic groups and number theory. Zbl 0806.11002 Platonov, V. P.; Rapinchuk, A. S. 143 1992 Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027 Platonov, V. P.; Rapinchuk, A. S. 71 1991 Weakly commensurable arithmetic groups and isospectral locally symmetric spaces. Zbl 1176.22011 Prasad, Gopal; Rapinchuk, Andrei S. 44 2009 Computation of the metaplectic kernel. Zbl 0941.22019 Prasad, Gopal; Rapinchuk, Andrei S. 30 1996 Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Zbl 1008.16018 Rapinchuk, Andrei S.; Segev, Yoav; Seitz, Gary M. 28 2002 Representation varieties of the fundamental groups of compact orientable surfaces. Zbl 0857.14012 Rapinchuk, A. S.; Benyash-Krivetz, V. V.; Chernousov, V. I. 26 1996 Existence of irreducible \(\mathbb R\)-regular elements in Zariski-dense subgroups. Zbl 1029.22020 Prasad, Gopal; Rapinchuk, Andrei S. 25 2003 On the existence of isotropic forms of semi-simple algebraic groups over number fields with prescribed local behavior. Zbl 1132.20024 Prasad, Gopal; Rapinchuk, Andrei S. 21 2006 Local-global principles for embedding of fields with involution into simple algebras with involution. Zbl 1223.11047 Prasad, Gopal; Rapinchuk, Andrei S. 20 2010 Torus bundles not distinguished by TQFT invariants. With an appendix by Louis Funar and Andrei Rapinchuk. Zbl 1278.57020 Funar, Louis 18 2013 Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025 Platonov, V. P.; Rapinchuk, A. S. 16 1992 Bounded generation of \(S\)-arithmetic subgroups of isotropic orthogonal groups over number fields. Zbl 1168.20020 Erovenko, Igor V.; Rapinchuk, Andrei S. 15 2006 Strong approximation for algebraic groups. Zbl 1341.20042 Rapinchuk, Andrei S. 14 2014 On division algebras having the same maximal subfields. Zbl 1205.16015 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 14 2010 The congruence subgroup property for \(\operatorname{Aut} F_2\): a group-theoretic proof of Asada’s theorem. Zbl 1251.20035 Bux, Kai-Uwe; Ershov, Mikhail V.; Rapinchuk, Andrei S. 14 2011 Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces. Zbl 1347.20053 Prasad, Gopal; Rapinchuk, Andrei S. 13 2014 Bounded generation of \(\mathrm{SL}_2\) over rings of \(S\)-integers with infinitely many units. Zbl 1448.11198 Morgan, Aleksander; Rapinchuk, Andrei; Sury, Balasubramanian 13 2018 The genus of a division algebra and the unramified Brauer group. Zbl 1293.16015 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 13 2013 Irreducible tori in semisimple groups. Zbl 1057.22025 Prasad, Gopal; Rapinchuk, Andrei S. 12 2001 Spinor groups with good reduction. Zbl 1443.11031 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 12 2019 The multinorm principle for linearly disjoint Galois extensions. Zbl 1309.11078 Pollio, Timothy P.; Rapinchuk, Andrei S. 12 2013 The finiteness of the genus of a finite-dimensional division algebra, and some generalizations. Zbl 1467.16018 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 12 2020 Valuation-like maps and the congruence subgroup property. Zbl 0999.16016 Rapinchuk, Andrei S.; Segev, Yoav 11 2001 Division algebras with the same maximal subfields. Zbl 1325.12006 Chernousov, V. I.; Rapinchuk, A. S.; Rapinchuk, I. A. 11 2015 On some finiteness properties of algebraic groups over finitely generated fields. (Sur quelques propriétés de finitude des groupes algébriques sur des corps de type fini.) Zbl 1376.14049 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2016 Bounded generation of some \(S\)-arithmetic orthogonal groups. Zbl 1010.20033 Erovenko, Igor V.; Rapinchuk, Andrei S. 9 2001 Zariski-dense subgroups and transcendental number theory. Zbl 1072.22009 Prasad, Gopal; Rapinchuk, Andrei S. 9 2005 On the size of the genus of a division algebra. Zbl 1356.16013 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 9 2016 The congruence problem for arithmetic groups of finite width. Zbl 0745.20043 Rapinchuk, A. S. 8 1990 Congruence subgroup problem for algebraic groups: Old and new. Zbl 0805.20040 Rapinchuk, A. S. 8 1992 On the genus of a division algebra. Zbl 1272.16020 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 8 2012 Associative algebras. (Assotsiativnye algebry). Transl. from the English by A. S. Rapinchuk and V. I. Yanchevskij. Transl. ed. and with a preface by A. E. Zalesskij. Zbl 0671.16001 Pierce, Richard S. 7 1986 Low-dimensional linear representations of \(\operatorname{Aut} F_n\), \(n\geq 3\). Zbl 0942.20002 Potapchik, A.; Rapinchuk, A. 7 2000 On the group of rational points of three-dimensional groups. Zbl 0431.12012 Platonov, V. P.; Rapinchuk, A. S. 7 1979 Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. Zbl 1285.20045 Garibaldi, Skip; Rapinchuk, Andrei 7 2013 Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups. Zbl 0879.20027 Rapinchuk, Andrei; Potapchik, Alexander 6 1996 On \(SS\)-rigid groups and A. Weil’s criterion for local rigidity. I. Zbl 0920.20004 Rapinchuk, A. S. 6 1998 The congruence subgroup problem. Zbl 1125.20313 Rapinchuk, A. S. 6 1999 Linear algebraic groups with good reduction. Zbl 1466.20032 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 6 2020 Non-virtually abelian anisotropic linear groups are not boundedly generated. Zbl 1491.11045 Corvaja, Pietro; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 6 2022 Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields. Zbl 1489.11059 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 6 2022 The congruence subgroup problem for algebraic groups. Zbl 0725.20034 Rapinchuk, A. 5 1990 Generic elements of a Zariski-dense subgroup form an open subset. Zbl 1423.22015 Prasad, G.; Rapinchuk, A. S. 5 2017 On the fields generated by the lengths of closed geodesics in locally symmetric spaces. Zbl 1308.53077 Prasad, Gopal; Rapinchuk, Andrei S. 5 2014 Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank \(> 1\) over Noetherian rings. Zbl 1232.19001 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 5 2011 Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010 Platonov, V. P.; Rapinchuk, A. S. 4 1984 On abstract homomorphisms of Chevalley groups with nonreductive image. I. Zbl 0987.20025 Lifschitz, L.; Rapinchuk, A. 4 2001 On the finite dimensional unitary representations of Kazhdan groups. Zbl 0926.22001 Rapinchuk, A. 4 1999 Multiplicative arithmetic of division algebras over number fields, and the metaplectic problem. Zbl 0678.20031 Rapinchuk, A. S. 4 1988 Subnormal subgroups of the groups of rational points of reductive algebraic groups. Zbl 1007.20043 Prasad, Gopal; Rapinchuk, Andrei S. 4 2002 On the congruence kernel for simple algebraic groups. Zbl 1356.20031 Prasad, Gopal; Rapinchuk, Andrei S. 4 2016 Towards the eigenvalue rigidity of Zariski-dense subgroups. Zbl 1373.20063 Rapinchuk, Andrei S. 4 2014 Class number of algebraic groups. Zbl 0425.20038 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 3 1979 The congruence problem for algebraic groups and strong approximations in affine varieties. Zbl 0661.20034 Rapinchuk, A. S. 3 1988 Algebraic groups. Zbl 0564.20023 Platonov, V. P.; Rapinchuk, A. S. 3 1983 The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029 Platonov, V. P.; Rapinchuk, A. S. 3 1982 The geometric theory of representations for the fundamental groups of compact oriented surfaces. Zbl 0840.20031 Rapinchuk, A. S.; Benyash-Krivets, V. V. 3 1993 On the congruence problem for algebraic groups. Zbl 0692.20033 Rapinchuk, A. S. 3 1989 Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties. Zbl 1537.11050 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 3 2023 The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups. Zbl 1101.20027 Rapinchuk, Andrei S. 3 2006 Representations of groups of finite width. Zbl 0777.20014 Rapinchuk, A. S. 2 1990 Platonov’s conjecture on the genus in arithmetic groups. Zbl 0477.20027 Rapinchuk, A. S. 2 1981 The Hasse principle for symmetric spaces. Zbl 0679.14027 Rapinchuk, A. S. 2 1987 Number-theoretic techniques in the theory of Lie groups and differential geometry. Zbl 1209.22006 Prasad, Gopal; Rapinchuk, Andrei S. 2 2010 Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction. Zbl 1547.11052 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 2 2024 Finiteness theorems for algebraic tori over function fields. Zbl 1473.14093 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 2 2021 Algebraic groups and number theory. Volume 1. 2nd revised edition of the book originally published in one volume. Zbl 1520.20002 Platonov, Vladimir; Rapinchuk, Andrei; Rapinchuk, Igor 2 2023 Division algebras with common subfields. Zbl 1532.16015 Krashen, Daniel; Matzri, Eliyahu; Rapinchuk, Andrei; Rowen, Louis; Saltman, David 2 2022 Multiplicative arithmetic of division algebras over number fields and the metaplectic problem. Zbl 0631.20034 Rapinchuk, A. S. 1 1987 Class numbers and groups of algebraic groups. II. Zbl 0464.20031 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1981 Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Class numbers and groups of algebraic groups. Zbl 0448.20045 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Class numbers in the genus of quadratic forms and algebraic groups. Zbl 0473.20032 Rapinchuk, A. S. 1 1981 Erratum: Irreducible tori in semisimple groups. Zbl 1099.22501 Prasad, Gopal; Rapinchuk, Andrei S. 1 2002 On the estimation of the number of double classes of adele groups of algebraic groups. Zbl 0393.20031 Bondarenko, A. A.; Rapincuk, A. S. 1 1978 Nonabelian free subgroups in homomorphic images of valued quaternion division algebras. Zbl 1117.16007 Rapinchuk, Andrei S.; Rowen, Louis; Segev, Yoav 1 2006 Bounded generation by semi-simple elements: quantitative results. (Engendrement borné par éléments semi-simples: résultats quantitatifs.) Zbl 1519.11016 Corvaja, Pietro; Demeio, Julian L.; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 1 2022 \(n\)-dimensional linear representations of \(\operatorname{Aut} F_ n\), and more. Zbl 0891.20024 Rapinchuk, Andrei S. 1 1997 Recent developments in the theory of linear algebraic groups: good reduction and finiteness properties. Zbl 1496.20080 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 1 2021 Applications of the fixed point theorem for group actions on buildings to algebraic groups over polynomial rings. Zbl 07877985 Abramenko, Peter; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 1 2024 Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction. Zbl 1547.11052 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 2 2024 Applications of the fixed point theorem for group actions on buildings to algebraic groups over polynomial rings. Zbl 07877985 Abramenko, Peter; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 1 2024 Properness of the global-to-local map for algebraic groups with toric connected component and other finiteness properties. Zbl 1537.11050 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 3 2023 Algebraic groups and number theory. Volume 1. 2nd revised edition of the book originally published in one volume. Zbl 1520.20002 Platonov, Vladimir; Rapinchuk, Andrei; Rapinchuk, Igor 2 2023 Non-virtually abelian anisotropic linear groups are not boundedly generated. Zbl 1491.11045 Corvaja, Pietro; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 6 2022 Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields. Zbl 1489.11059 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 6 2022 Division algebras with common subfields. Zbl 1532.16015 Krashen, Daniel; Matzri, Eliyahu; Rapinchuk, Andrei; Rowen, Louis; Saltman, David 2 2022 Bounded generation by semi-simple elements: quantitative results. (Engendrement borné par éléments semi-simples: résultats quantitatifs.) Zbl 1519.11016 Corvaja, Pietro; Demeio, Julian L.; Rapinchuk, Andrei S.; Ren, Jinbo; Zannier, Umberto M. 1 2022 Finiteness theorems for algebraic tori over function fields. Zbl 1473.14093 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 2 2021 Recent developments in the theory of linear algebraic groups: good reduction and finiteness properties. Zbl 1496.20080 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 1 2021 The finiteness of the genus of a finite-dimensional division algebra, and some generalizations. Zbl 1467.16018 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 12 2020 Linear algebraic groups with good reduction. Zbl 1466.20032 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 6 2020 Spinor groups with good reduction. Zbl 1443.11031 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 12 2019 Bounded generation of \(\mathrm{SL}_2\) over rings of \(S\)-integers with infinitely many units. Zbl 1448.11198 Morgan, Aleksander; Rapinchuk, Andrei; Sury, Balasubramanian 13 2018 Generic elements of a Zariski-dense subgroup form an open subset. Zbl 1423.22015 Prasad, G.; Rapinchuk, A. S. 5 2017 On some finiteness properties of algebraic groups over finitely generated fields. (Sur quelques propriétés de finitude des groupes algébriques sur des corps de type fini.) Zbl 1376.14049 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 10 2016 On the size of the genus of a division algebra. Zbl 1356.16013 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 9 2016 On the congruence kernel for simple algebraic groups. Zbl 1356.20031 Prasad, Gopal; Rapinchuk, Andrei S. 4 2016 Division algebras with the same maximal subfields. Zbl 1325.12006 Chernousov, V. I.; Rapinchuk, A. S.; Rapinchuk, I. A. 11 2015 Strong approximation for algebraic groups. Zbl 1341.20042 Rapinchuk, Andrei S. 14 2014 Generic elements in Zariski-dense subgroups and isospectral locally symmetric spaces. Zbl 1347.20053 Prasad, Gopal; Rapinchuk, Andrei S. 13 2014 On the fields generated by the lengths of closed geodesics in locally symmetric spaces. Zbl 1308.53077 Prasad, Gopal; Rapinchuk, Andrei S. 5 2014 Towards the eigenvalue rigidity of Zariski-dense subgroups. Zbl 1373.20063 Rapinchuk, Andrei S. 4 2014 Torus bundles not distinguished by TQFT invariants. With an appendix by Louis Funar and Andrei Rapinchuk. Zbl 1278.57020 Funar, Louis 18 2013 The genus of a division algebra and the unramified Brauer group. Zbl 1293.16015 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 13 2013 The multinorm principle for linearly disjoint Galois extensions. Zbl 1309.11078 Pollio, Timothy P.; Rapinchuk, Andrei S. 12 2013 Weakly commensurable \(S\)-arithmetic subgroups in almost simple algebraic groups of types B and C. Zbl 1285.20045 Garibaldi, Skip; Rapinchuk, Andrei 7 2013 On the genus of a division algebra. Zbl 1272.16020 Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. 8 2012 The congruence subgroup property for \(\operatorname{Aut} F_2\): a group-theoretic proof of Asada’s theorem. Zbl 1251.20035 Bux, Kai-Uwe; Ershov, Mikhail V.; Rapinchuk, Andrei S. 14 2011 Centrality of the congruence kernel for elementary subgroups of Chevalley groups of rank \(> 1\) over Noetherian rings. Zbl 1232.19001 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 5 2011 Local-global principles for embedding of fields with involution into simple algebras with involution. Zbl 1223.11047 Prasad, Gopal; Rapinchuk, Andrei S. 20 2010 On division algebras having the same maximal subfields. Zbl 1205.16015 Rapinchuk, Andrei S.; Rapinchuk, Igor A. 14 2010 Number-theoretic techniques in the theory of Lie groups and differential geometry. Zbl 1209.22006 Prasad, Gopal; Rapinchuk, Andrei S. 2 2010 Weakly commensurable arithmetic groups and isospectral locally symmetric spaces. Zbl 1176.22011 Prasad, Gopal; Rapinchuk, Andrei S. 44 2009 On the existence of isotropic forms of semi-simple algebraic groups over number fields with prescribed local behavior. Zbl 1132.20024 Prasad, Gopal; Rapinchuk, Andrei S. 21 2006 Bounded generation of \(S\)-arithmetic subgroups of isotropic orthogonal groups over number fields. Zbl 1168.20020 Erovenko, Igor V.; Rapinchuk, Andrei S. 15 2006 The Margulis-Platonov conjecture for \(\text{SL}_{1,D}\) and 2-generation of finite simple groups. Zbl 1101.20027 Rapinchuk, Andrei S. 3 2006 Nonabelian free subgroups in homomorphic images of valued quaternion division algebras. Zbl 1117.16007 Rapinchuk, Andrei S.; Rowen, Louis; Segev, Yoav 1 2006 Zariski-dense subgroups and transcendental number theory. Zbl 1072.22009 Prasad, Gopal; Rapinchuk, Andrei S. 9 2005 Existence of irreducible \(\mathbb R\)-regular elements in Zariski-dense subgroups. Zbl 1029.22020 Prasad, Gopal; Rapinchuk, Andrei S. 25 2003 Finite quotients of the multiplicative group of a finite dimensional division algebra are solvable. Zbl 1008.16018 Rapinchuk, Andrei S.; Segev, Yoav; Seitz, Gary M. 28 2002 Subnormal subgroups of the groups of rational points of reductive algebraic groups. Zbl 1007.20043 Prasad, Gopal; Rapinchuk, Andrei S. 4 2002 Erratum: Irreducible tori in semisimple groups. Zbl 1099.22501 Prasad, Gopal; Rapinchuk, Andrei S. 1 2002 Irreducible tori in semisimple groups. Zbl 1057.22025 Prasad, Gopal; Rapinchuk, Andrei S. 12 2001 Valuation-like maps and the congruence subgroup property. Zbl 0999.16016 Rapinchuk, Andrei S.; Segev, Yoav 11 2001 Bounded generation of some \(S\)-arithmetic orthogonal groups. Zbl 1010.20033 Erovenko, Igor V.; Rapinchuk, Andrei S. 9 2001 On abstract homomorphisms of Chevalley groups with nonreductive image. I. Zbl 0987.20025 Lifschitz, L.; Rapinchuk, A. 4 2001 Low-dimensional linear representations of \(\operatorname{Aut} F_n\), \(n\geq 3\). Zbl 0942.20002 Potapchik, A.; Rapinchuk, A. 7 2000 The congruence subgroup problem. Zbl 1125.20313 Rapinchuk, A. S. 6 1999 On the finite dimensional unitary representations of Kazhdan groups. Zbl 0926.22001 Rapinchuk, A. 4 1999 On \(SS\)-rigid groups and A. Weil’s criterion for local rigidity. I. Zbl 0920.20004 Rapinchuk, A. S. 6 1998 \(n\)-dimensional linear representations of \(\operatorname{Aut} F_ n\), and more. Zbl 0891.20024 Rapinchuk, Andrei S. 1 1997 Computation of the metaplectic kernel. Zbl 0941.22019 Prasad, Gopal; Rapinchuk, Andrei S. 30 1996 Representation varieties of the fundamental groups of compact orientable surfaces. Zbl 0857.14012 Rapinchuk, A. S.; Benyash-Krivetz, V. V.; Chernousov, V. I. 26 1996 Normal subgroups of \(SL_{1,D}\) and the classification of finite simple groups. Zbl 0879.20027 Rapinchuk, Andrei; Potapchik, Alexander 6 1996 Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046 Platonov, Vladimir; Rapinchuk, Andrei 368 1994 The geometric theory of representations for the fundamental groups of compact oriented surfaces. Zbl 0840.20031 Rapinchuk, A. S.; Benyash-Krivets, V. V. 3 1993 Algebraic groups and number theory. Zbl 0806.11002 Platonov, V. P.; Rapinchuk, A. S. 143 1992 Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025 Platonov, V. P.; Rapinchuk, A. S. 16 1992 Congruence subgroup problem for algebraic groups: Old and new. Zbl 0805.20040 Rapinchuk, A. S. 8 1992 Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027 Platonov, V. P.; Rapinchuk, A. S. 71 1991 The congruence problem for arithmetic groups of finite width. Zbl 0745.20043 Rapinchuk, A. S. 8 1990 The congruence subgroup problem for algebraic groups. Zbl 0725.20034 Rapinchuk, A. 5 1990 Representations of groups of finite width. Zbl 0777.20014 Rapinchuk, A. S. 2 1990 On the congruence problem for algebraic groups. Zbl 0692.20033 Rapinchuk, A. S. 3 1989 Multiplicative arithmetic of division algebras over number fields, and the metaplectic problem. Zbl 0678.20031 Rapinchuk, A. S. 4 1988 The congruence problem for algebraic groups and strong approximations in affine varieties. Zbl 0661.20034 Rapinchuk, A. S. 3 1988 The Hasse principle for symmetric spaces. Zbl 0679.14027 Rapinchuk, A. S. 2 1987 Multiplicative arithmetic of division algebras over number fields and the metaplectic problem. Zbl 0631.20034 Rapinchuk, A. S. 1 1987 Associative algebras. (Assotsiativnye algebry). Transl. from the English by A. S. Rapinchuk and V. I. Yanchevskij. Transl. ed. and with a preface by A. E. Zalesskij. Zbl 0671.16001 Pierce, Richard S. 7 1986 Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010 Platonov, V. P.; Rapinchuk, A. S. 4 1984 Algebraic groups. Zbl 0564.20023 Platonov, V. P.; Rapinchuk, A. S. 3 1983 The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029 Platonov, V. P.; Rapinchuk, A. S. 3 1982 Platonov’s conjecture on the genus in arithmetic groups. Zbl 0477.20027 Rapinchuk, A. S. 2 1981 Class numbers and groups of algebraic groups. II. Zbl 0464.20031 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1981 Class numbers in the genus of quadratic forms and algebraic groups. Zbl 0473.20032 Rapinchuk, A. S. 1 1981 Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Class numbers and groups of algebraic groups. Zbl 0448.20045 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 On the group of rational points of three-dimensional groups. Zbl 0431.12012 Platonov, V. P.; Rapinchuk, A. S. 7 1979 Class number of algebraic groups. Zbl 0425.20038 Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 3 1979 On the estimation of the number of double classes of adele groups of algebraic groups. Zbl 0393.20031 Bondarenko, A. A.; Rapincuk, A. S. 1 1978 all cited Publications top 5 cited Publications all top 5 Cited by 817 Authors 38 Rapinchuk, Andrei S. 21 Lubotzky, Alexander 20 Rapinchuk, Igor A. 18 Nguyễn Quôc Thăng 15 Chernousov, Vladimir I. 10 Oh, Hee 10 Parimala, Raman 10 Prasad, Gopal 10 Yu, Chia-Fu 9 Avni, Nir 9 Einsiedler, Manfred Leopold 9 Gorodnik, Alexander 9 Linowitz, Benjamin 8 Garibaldi, Skip 8 Margulis, Grigoriĭ Aleksandrovich 8 McReynolds, David Ben 8 Mohammadi, Amir 7 Aka, Menny 7 Bayer-Fluckiger, Eva 7 Belolipetsky, Mikhail V. 7 Borovoi, Mikhail V. 7 Gelander, Tsachik 7 Kammeyer, Holger 7 Xu, Fei 6 Benyash-Krivets, Valeriĭ Vatslavovich 6 Gille, Philippe 6 Gordeev, Nikolai L. 6 Grunewald, Fritz J. 6 Kaletha, Tasho 6 Kunyavskiĭ, Boris Èmmanuilovich 6 Larsen, Michael Jeffrey 6 Segev, Yoav 6 Shapira, Uri 6 Vavilov, Nikolaĭ Aleksandrovich 6 Venkataramana, Tyakal Nanjundiah 6 Wei, Dasheng 6 Witte Morris, Dave 6 Yafaev, Andrei 5 Ben-Ezra, David El-Chai 5 Cao, Yang 5 Fiori, Andrew 5 Loughran, Daniel 5 Pillay, Anand 5 Sarnak, Peter Clive 5 Shah, Nimish A. 5 Shin, Sug Woo 5 Stover, Matthew 5 Sury, Balasubramanian 5 Ullmo, Emmanuel 5 Vishne, Uzi 5 Wakatsuki, Satoshi 5 Zalesskii, Pavel 4 Arenas-Carmona, Luis 4 Bitan, Rony A. 4 Breuillard, Emmanuel 4 Bridson, Martin R. 4 Chan, Wai Kiu 4 Choiy, Kwangho 4 Colliot-Thélène, Jean-Louis 4 Emery, Vincent 4 Fisher, David Michael 4 Krashen, Daniel 4 Lee, Tingyu 4 Levit, Arie 4 Liebeck, Martin Walter 4 Lindenstrauss, Elon 4 Meyer, Jeffrey S. 4 Nevo, Amos 4 Platonov, Vladimir Petrovich 4 Plotkin, Eugene 4 Reid, Alan W. 4 Richard, Rodolphe 4 Rowen, Louis Halle 4 Rühr, Rene 4 Salehi Golsefidy, Alireza 4 Sauer, Roman 4 Thakur, Maneesh L. 4 Venkatesh, Akshay 4 Wieser, Andreas 4 Wortman, Kevin A. 3 Admiralova, Aleksandra Nikolaevna 3 Bader, Uri 3 Bekka, Mohammed el Bachir 3 Benoist, Yves 3 Bou-Rabee, Khalid 3 Bundy, David M. 3 del Río, Angel 3 Detinko, Alla S. 3 Flicker, Yuval Z. 3 Gao, Ziyang 3 Glasner, Yair 3 Gross, Benedict Hyman 3 Gvozdevsky, Pavel 3 Hooda, Neha 3 Hoshi, Akinari 3 Jaikin-Zapirain, Andrei 3 Kanai, Kazuki 3 Kim, Henry H. 3 Kim, Inkang 3 Klopsch, Benjamin ...and 717 more Authors all top 5 Cited in 161 Serials 55 Journal of Algebra 34 Israel Journal of Mathematics 33 Duke Mathematical Journal 28 Journal of Number Theory 28 Transactions of the American Mathematical Society 24 Mathematische Zeitschrift 24 Proceedings of the American Mathematical Society 23 Advances in Mathematics 21 Inventiones Mathematicae 15 Compositio Mathematica 15 Geometriae Dedicata 15 Mathematische Annalen 15 Annals of Mathematics. Second Series 12 Journal of Pure and Applied Algebra 12 Michigan Mathematical Journal 12 Geometric and Functional Analysis. GAFA 12 Forum of Mathematics, Sigma 11 Journal of Mathematical Sciences (New York) 11 Journal of the European Mathematical Society (JEMS) 11 Algebra & Number Theory 10 Communications in Algebra 10 Journal of the American Mathematical Society 9 Annales de l’Institut Fourier 9 Ergodic Theory and Dynamical Systems 8 Publications Mathématiques 8 Journal of the London Mathematical Society. Second Series 8 Journal für die Reine und Angewandte Mathematik 8 Manuscripta Mathematica 8 Proceedings of the London Mathematical Society. Third Series 8 Proceedings of the Steklov Institute of Mathematics 7 Memoirs of the American Mathematical Society 7 Comptes Rendus. Mathématique. Académie des Sciences, Paris 6 Journal d’Analyse Mathématique 6 International Journal of Algebra and Computation 6 Documenta Mathematica 6 Transformation Groups 6 Geometry & Topology 6 Journal of Group Theory 6 Algebraic & Geometric Topology 6 International Journal of Number Theory 6 Journal of Modern Dynamics 6 European Journal of Mathematics 5 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 5 Bulletin of the London Mathematical Society 5 Nagoya Mathematical Journal 5 Journal de Théorie des Nombres de Bordeaux 5 Representation Theory 5 Journal of the Institute of Mathematics of Jussieu 5 Journal of Algebra and its Applications 4 Mathematical Proceedings of the Cambridge Philosophical Society 4 Archiv der Mathematik 4 Mathematika 4 Pacific Journal of Mathematics 4 Annals of Pure and Applied Logic 4 Groups, Geometry, and Dynamics 3 Mathematical Notes 3 Commentarii Mathematici Helvetici 3 Journal of the Mathematical Society of Japan 3 Journal of Soviet Mathematics 3 The Journal of Symbolic Logic 3 Monatshefte für Mathematik 3 Proceedings of the Japan Academy. Series A 3 Siberian Mathematical Journal 3 Forum Mathematicum 3 International Journal of Mathematics 3 Bulletin of the American Mathematical Society. New Series 3 Doklady Mathematics 3 Trudy Instituta Matematiki 3 Forum of Mathematics, Pi 3 Journal de l’École Polytechnique – Mathématiques 2 Communications in Mathematical Physics 2 Linear and Multilinear Algebra 2 Russian Mathematical Surveys 2 Mathematics of Computation 2 Acta Arithmetica 2 Bulletin de la Société Mathématique de France 2 Canadian Journal of Mathematics 2 Canadian Mathematical Bulletin 2 Functiones et Approximatio. Commentarii Mathematici 2 Indiana University Mathematics Journal 2 Journal of Functional Analysis 2 Topology and its Applications 2 European Journal of Combinatorics 2 IMRN. International Mathematics Research Notices 2 Linear Algebra and its Applications 2 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 2 Annales de la Faculté des Sciences de Toulouse. Mathématiques. Série VI 2 Experimental Mathematics 2 Journal of Algebraic Geometry 2 Journal of Lie Theory 2 Bulletin des Sciences Mathématiques 2 Journal of the Australian Mathematical Society 2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 2 Journal of Noncommutative Geometry 2 Albanian Journal of Mathematics 2 Kyoto Journal of Mathematics 2 Research in Number Theory 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 Nonlinearity ...and 61 more Serials all top 5 Cited in 41 Fields 415 Number theory (11-XX) 396 Group theory and generalizations (20-XX) 223 Topological groups, Lie groups (22-XX) 208 Algebraic geometry (14-XX) 79 Dynamical systems and ergodic theory (37-XX) 55 Associative rings and algebras (16-XX) 55 Manifolds and cell complexes (57-XX) 44 Field theory and polynomials (12-XX) 42 Differential geometry (53-XX) 29 Combinatorics (05-XX) 24 Nonassociative rings and algebras (17-XX) 21 Global analysis, analysis on manifolds (58-XX) 20 Mathematical logic and foundations (03-XX) 20 \(K\)-theory (19-XX) 17 Geometry (51-XX) 15 Several complex variables and analytic spaces (32-XX) 11 Functions of a complex variable (30-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 9 Category theory; homological algebra (18-XX) 9 Functional analysis (46-XX) 7 Commutative algebra (13-XX) 7 Abstract harmonic analysis (43-XX) 7 Algebraic topology (55-XX) 6 Measure and integration (28-XX) 5 Convex and discrete geometry (52-XX) 5 Probability theory and stochastic processes (60-XX) 3 Computer science (68-XX) 3 Quantum theory (81-XX) 3 Information and communication theory, circuits (94-XX) 2 General and overarching topics; collections (00-XX) 2 Order, lattices, ordered algebraic structures (06-XX) 2 General topology (54-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Ordinary differential equations (34-XX) 1 Partial differential equations (35-XX) 1 Difference and functional equations (39-XX) 1 Harmonic analysis on Euclidean spaces (42-XX) 1 Operator theory (47-XX) 1 Numerical analysis (65-XX) 1 Relativity and gravitational theory (83-XX) 1 Biology and other natural sciences (92-XX) Citations by Year