Edit Profile (opens in new tab) Platonov, Vladimir Petrovich Compute Distance To: Compute Author ID: platonov.vladimir-p Published as: Platonov, V. P.; Platonov, Vladimir P.; Platonov, Vladimir; Platonov, Vladimir Petrovich; Platonov, V. more...less Further Spellings: Platonaŭ, Uladzimir Pyatrovich; Platonaŭ, Uladzimir Pyatrovich; Платонаў Уладзімір Пятровіч; Платонаў Уладзімір Пятровіч External Links: MGP · Wikidata · Math-Net.Ru · GND · IdRef Documents Indexed: 187 Publications since 1962, including 2 Books 2 Contributions as Editor Biographic References: 8 Publications Co-Authors: 83 Co-Authors with 100 Joint Publications 3,033 Co-Co-Authors all top 5 Co-Authors 88 single-authored 16 Petrunin, Maksim Maksimovich 16 Rapinchuk, Andrei S. 13 Yanchevskii, Vyacheslav Ivanovich 11 Fëdorov, Gleb Vladimirovich 8 Benyash-Krivets, Valeriĭ Vatslavovich 6 Grunewald, Fritz J. 5 Zhgoon, Vladimir S. 4 Bondarenko, Aleksandr Adamovich 4 Chernousov, Vladimir I. 4 Đoković, Dragomir Ž. 4 Parshin, Alexei N. 4 Shteĭnikov, Yuriĭ Nikolaevich 3 Drakokhrust, Yu. A. 2 Bokut, Leonid A. 2 Kac, Victor G. 2 Novikov, Sergeĭ Petrovich 2 Shestakov, Ivan Pavlovich 2 Taimanov, Iskander Asanovich 2 Tavgen’, Oleg Ignat’evich 2 Zalesski, Alexandre Efimovich 1 Afendikov, Andrei L. 1 Aptekarev, Alexander Ivanovich 1 Arkhipov, Gennadiĭ Ivanovich 1 Avdeev, F. S. 1 Borel, Armand 1 Bukhshtaber, Viktor Matveevich 1 Chirskiĭ, Vladimir Grigor’evich 1 Dobrovol’skiĭ, Nikolaĭ Mikhaĭlovich 1 Faddeev, Lyudvig Dmitrievich 1 Fomenko, Anatoliĭ Timofeevich 1 Gashkov, Sergey B. 1 Godunov, Sergeĭ Konstantinovich 1 Golod, Evgeniĭ Solomonovich 1 Grigorchuk, Rostislav Ivanovich 1 Kashin, Boris Sergeevich 1 Kemer, Aleksandr Robertovich 1 Kharchenko, Vladislav K. 1 Kharlampovich, Olga G. 1 Kolesnikov, Pavel Sergeevich 1 Konyukh, V. S. 1 Kozlov, Valeriĭ Vasil’evich 1 Kutateladze, Semën Samsonovich 1 Kyrychenko, Volodymyr Vasyl’ovych 1 Latyshev, Viktor Nikolaevich 1 Makar-Limanov, Leonid G. 1 Mal’tsev, Yuriĭ Nikolaevich 1 Manin, Yuri Ivanovich 1 Margulis, Grigoriĭ Aleksandrovich 1 Maslov, A. I. 1 Matveev, Gennadiĭ Vasil’evich 1 Mel’nikov, I. I. 1 Mikhalëv, Aleksandr Vasil’evich 1 Milovanov, M. V. 1 Mineev, Mikhail Petrovich 1 Myasnikov, Alexei G. 1 Nesterenko, Yuriĭ Valentinovich 1 Nguyen Quoc Thi 1 Nikol’skiĭ, Sergeĭ Mikhaĭlovich 1 Ol’shanskiĭ, Aleksandr Yur’evich 1 Panin, Ivan A. 1 Panov, Aleksandr Nikolaevich 1 Popov, Vladimir Leonidovich 1 Potapchik, Alexander 1 Prokhorov, Yuriĭ Vasil’evich 1 Reshetnyak, Yuriĭ Grigor’evich 1 Romanovskii, N. S. 1 Sadovnichiĭ, Viktor Antonovich 1 Saromet, A. A. 1 Sharomet, A. A. 1 Shevrin, Lev Naumovich 1 Strunkov, S. P. 1 Suprunenko, Dmitrii Alexeevich 1 Sury, Balasubramanian 1 Tishkin, Vladimir Fëdorovich 1 Umirbaev, Ualbaĭ Utmakhanbetovich 1 Vavilov, Nikolaĭ Aleksandrovich 1 Vinberg, Èrnest Borisovich 1 Yakovlev, Anatoliĭ Vladimirovich 1 Yanovich, Leonid Aleksandrovich 1 Zel’manov, Efim Isaakovich 1 Zhelyabin, Viktor Nikolaevich 1 Zhgun, V. S. 1 Zhizhchenko, Alexey B. 1 Zusmanovich, Pasha all top 5 Serials 38 Soviet Mathematics. Doklady 26 Doklady Mathematics 19 Doklady Akademii Nauk BSSR 15 Russian Mathematical Surveys 9 Mathematics of the USSR. Izvestiya 8 Proceedings of the Steklov Institute of Mathematics 6 Izvestiya Akademii Nauk SSSR. Seriya Matematicheskaya 4 Izvestiya Akademii Nauk BSSR. Seriya Fiziko-Matematicheskikh Nauk 3 Sibirskiĭ Matematicheskiĭ Zhurnal 3 Mathematics of the USSR, Sbornik 3 Comptes Rendus de l’Académie des Sciences. Série I 3 Sbornik: Mathematics 3 Comptes Rendus de l’Académie des Sciences. Série I. Mathématique 3 Chebyshevskiĭ Sbornik 3 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 3 Translations. Series 2. American Mathematical Society 2 Doklady Akademii Nauk SSSR 2 Journal of Algebra 2 Journal of Soviet Mathematics 2 Matematicheskiĭ Sbornik. Novaya Seriya 2 Siberian Mathematical Journal 1 Mathematical Notes 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Duke Mathematical Journal 1 Journal für die Reine und Angewandte Mathematik 1 Manuscripta Mathematica 1 Mathematische Annalen 1 Transactions of the American Mathematical Society 1 \(K\)-Theory 1 International Journal of Mathematics 1 Discrete Mathematics and Applications 1 Russian Academy of Sciences. Izvestiya. Mathematics 1 Izvestiya: Mathematics 1 Voprosy Algebry 1 Comptes Rendus. Mathématique. Académie des Sciences, Paris all top 5 Fields 100 Group theory and generalizations (20-XX) 71 Number theory (11-XX) 34 Associative rings and algebras (16-XX) 32 Algebraic geometry (14-XX) 14 Topological groups, Lie groups (22-XX) 10 Linear and multilinear algebra; matrix theory (15-XX) 8 History and biography (01-XX) 7 Field theory and polynomials (12-XX) 2 General and overarching topics; collections (00-XX) 2 Commutative algebra (13-XX) 2 Category theory; homological algebra (18-XX) 2 \(K\)-theory (19-XX) 1 Partial differential equations (35-XX) 1 General topology (54-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 131 Publications have been cited 1,058 times in 704 Documents Cited by ▼ Year ▼ Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046Platonov, Vladimir; Rapinchuk, Andrei 279 1994 Algebraic groups and number theory. Zbl 0806.11002Platonov, V. P.; Rapinchuk, A. S. 109 1992 Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027Platonov, V. P.; Rapinchuk, A. S. 49 1991 Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field. Zbl 1305.11096Platonov, V. P. 36 2014 Groups of \(S\)-units in hyperelliptic fields and continued fractions. Zbl 1231.11131Benyash-Krivets, V. V.; Platonov, V. P. 22 2009 On the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1445.11135Platonov, V. P.; Fedorov, G. V. 19 2018 The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups. Zbl 0217.36301Platonov, V. P. 18 1971 \(S\)-units and periodicity of continued fractions in hyperelliptic fields. Zbl 1337.11040Platonov, V. P.; Fedorov, G. V. 14 2015 Locally projectively nilpotent subgroups and nilelements in topological groups. Zbl 0222.22002Platonov, V. P. 14 1966 Linear preserver problems and algebraic groups. Zbl 0836.20065Platonov, Vladimir P.; Đoković, Dragomir Ž. 13 1995 Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1440.11127Platonov, V. P.; Petrunin, M. M. 13 2018 Continued rational fractions in hyperelliptic fields and the Mumford representation. Zbl 1403.11071Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V. 13 2016 On the periodicity of continued fractions in hyperelliptic fields. Zbl 1418.11109Platonov, V. P.; Fedorov, G. V. 13 2017 \(S\)-units in hyperelliptic fields and periodicity of continued fractions. Zbl 1392.11035Platonov, V. P.; Petrunin, M. M. 13 2016 \(S\)-units and periodicity in quadratic function fields. Zbl 1357.11111Platonov, V. P.; Petrunin, M. M. 13 2016 Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025Platonov, V. P.; Rapinchuk, A. S. 12 1992 Das Tannaka-Artinsche Problem und reduzierte K-Theorie. Zbl 0338.16005Platonov, V. P. 12 1976 The Tannaka-Artin problem and reduced K-theory. Zbl 0349.16008Platonov, V. P. 12 1977 Arithmetic theory of algebraic groups. Zbl 0502.20025Platonov, V. P. 11 1982 On the Tannaka-Artin problem. Zbl 0333.20032Platonov, V. P. 11 1975 On the periodicity of continued fractions in elliptic fields. Zbl 1392.11048Platonov, V. P.; Fedorov, G. V. 11 2017 New orders of torsion points in Jacobians of curves of genus 2 over the rational number field. Zbl 1319.11041Platonov, V. P.; Petrunin, M. M. 10 2012 Arithmetic of quadratic fields and torsion in Jacobians. Zbl 1217.11094Platonov, V. P. 10 2010 On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\). Zbl 1477.11187Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N. 8 2019 The Hasse norm principle for algebraic number fields. Zbl 0624.12009Drakokhrust, Yu. A.; Platonov, V. P. 8 1987 The rationality problem for semisimple group varieties. Zbl 0904.20036Chernousov, Vladimir I.; Platonov, Vladimir P. 8 1998 Engel elements and the radical in PI-algebras and topological groups. Zbl 0136.29503Platonov, V. P. 8 1965 On the group of rational points of three-dimensional groups. Zbl 0431.12012Platonov, V. P.; Rapinchuk, A. S. 7 1979 Linear algebraic groups. (Linejnye algebraicheskie gruppy.) Übersetzung aus dem Englischen von A. E. Zalesskii. Herausgegeben von V. P. Platonov. Zbl 0235.22017Borel, Armand 7 1972 On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\). Zbl 1428.11131Platonov, V. P.; Zhgoon, V. S.; Petrunin, M. M.; Shteinikov, Yu. N. 7 2018 Theory of algebraic linear groups and periodic groups. Zbl 0177.04802Platonov, V. P. 7 1968 Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves. Zbl 1348.14083Platonov, V. P.; Petrunin, M. M. 6 2015 On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field. Zbl 1443.11141Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V. 6 2018 On Grothendieck’s problem on profinite completions of groups. Zbl 0614.20016Platonov, V. P.; Tavgen’, O. I. 6 1986 Algebraic groups and reduced K-theory. Zbl 0425.16018Platonov, V. P. 6 1980 Subgroups of \(\text{GL}(n^ 2,\mathbf C)\) containing \(\text{PSU}(n)\). Zbl 0848.20033Platonov, V. P.; Đoković, D. Ž. 6 1996 Determination of algebraic groups by arithmetic subgroups. Zbl 0312.20024Platonov, V. P.; Milovanov, M. V. 6 1973 Rigidity results for groups with radical cohomology of finite groups and arithmeticity problems. Zbl 1007.11029Grunewald, Fritz; Platonov, Vladimir 6 1999 On finite extensions of arithmetic groups. Zbl 0913.20034Grunewald, Fritz; Platonov, Vladimir 6 1997 A proof of the finiteness hypothesis for solvable subgroups of algebraic groups. (Beweis der Endlichkeitshypothese für auflösbare Untergruppen algebraischer Gruppen.) Zbl 0182.04702Platonov, V. P. 6 1969 Algebraic groups and linear preserver problems. Zbl 0811.20044Đoković, Dragomir Ž.; Platonov, Vladimir P. 6 1993 A certain problem for finitely generated groups. Zbl 0228.20018Platonov, V. P. 6 1968 Rings and varieties of representations of finitely generated groups. Zbl 0765.20011Platonov, V. P. 5 1989 Character rings of representations of finitely generated groups. Zbl 0766.20008Platonov, V. P.; Benyash-Krivets, V. V. 5 1990 On the problem of classification of periodic continued fractions in hyperelliptic fields. Zbl 1451.11127Platonov, V. P.; Fedorov, G. V. 5 2020 The Frattini subgroup of linear groups and finite approximability. Zbl 0242.20038Platonov, V. P. 5 1966 Lokal projective nilpotent radicals in topological groups. Zbl 0242.22006Platonov, V. P. 5 1965 Low-dimensional representations of \(\text{Aut}(F_ 2)\). Zbl 0862.20006Đoković, Dragomir Ž.; Platonov, Vladimir P. 5 1996 The structure of unitary groups and the commutator group of a simple algebra over global fields. Zbl 0298.20035Platonov, V. P.; Yanchevskii, V. I. 5 1973 Die Unendlichkeit der reduzierten Whiteheadgruppe im Tannaka-Artin- Problem. Zbl 0352.16009Platonov, V. P. 5 1976 A new local-global principle for quadratic function fields. Zbl 1244.11093Benyash-Krivets, V. V.; Platonov, V. P. 5 2010 On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order. Zbl 1278.14045Platonov, V. P.; Zhgun, V. S.; Petrunin, M. M. 5 2013 Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010Platonov, V. P.; Rapinchuk, A. S. 4 1984 Dieudonné’s conjecture on the structure of unitary groups over a division ring, and Hermitian K-theory. Zbl 0593.16012Platonov, V. P.; Yanchevskij, V. I. 4 1985 On the rationality of canonical spinor varieties. Zbl 0486.14013Platonov, V. P.; Chernousov, V. I. 4 1980 On Harder’s conjecture. Zbl 0333.20035Platonov, V. P.; Yanchevskii, V. I. 4 1975 A problem of Tannaka-Artin and groups of projective conorms. Zbl 0338.16004Platonov, V. P. 4 1975 Solvable arithmetic groups and arithmeticity problems. Zbl 1039.20026Grunewald, Fritz; Platonov, Vladimir 4 1999 An infinite family of curves of genus 2 over the field of rational numbers whose Jacobian varieties contain rational points of order 28. Zbl 1427.14062Platonov, V. P.; Fedorov, G. V. 3 2018 The arithmetic theory of algebraic groups. Zbl 0513.20028Platonov, V. P. 3 1982 The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029Platonov, V. P.; Rapinchuk, A. S. 3 1982 Finite-dimensional Henselian division algebras. Zbl 0669.16016Platonov, V. P.; Yanchevskij, V. I. 3 1988 On the maximality problem for arithmetic groups. Zbl 0252.20050Platonov, V. P. 3 1971 On the Kneser-Tits conjecture for unitary groups. Zbl 0343.16016Platonov, V. P.; Yanchevskii, V. I. 3 1975 Continued fractions and \(S\)-units in hyperelliptic fields. Zbl 1225.11160Benyash-Krivets, V. V.; Platonov, V. P. 3 2008 Groups of \(S\)-units in hyperelliptic fields. Zbl 1154.11039Benyash-Krivets, V. V.; Platonov, V. P. 3 2007 Non-arithmetic polycyclic groups. Zbl 0974.20035Grunewald, Fritz; Platonov, Vladimir 3 1998 Structure of topological locally projectively nilpotent groups, and of groups with a normalizer condition. Zbl 0164.34203Platonov, V. P. 3 1968 Certain classes of topological groups. Zbl 0166.02701Platonov, V. P. 3 1966 The structure of periodic linear groups and algebraic groups. Zbl 0171.28802Platonov, V. P. 3 1966 Some remarks on linear groups. Zbl 0215.39701Platonov, V. P. 3 1968 On new properties of Hankel matrices over the field of rational numbers. Zbl 1432.11031Platonov, Vladimir P. 3 2017 Birational properties of the reduced Whitehead group. Zbl 0791.20045Platonov, V. P. 3 1977 On Auerbach’s problem. Zbl 0225.20025Platonov, V. P.; Zalesskij, A. E. 3 1966 Birational properties of spinor varieties. Zbl 0496.14008Platonov, V. P. 3 1981 New combinatorial properties of linear groups. Zbl 0983.20041Platonov, Vladimir P.; Potapchik, Alexander 3 2001 Subgroups of algebraic groups over a local or global field containing a maximal torus. Zbl 0831.20062Platonov, Vladimir P. 3 1994 On new arithmetic properties of determinants of Hankel matrices. Zbl 1400.15012Platonov, V. P.; Petrunin, M. M. 2 2018 Algebraic groups. Zbl 0564.20023Platonov, V. P.; Rapinchuk, A. S. 2 1983 On the theory of Henselian division algebras. Zbl 0667.16018Platonov, V. P.; Yanchevskij, V. I. 2 1988 Reduced K-theory and approximation in algebraic groups. Zbl 0417.16012Platonov, V. P. 2 1976 Class number of algebraic groups. Zbl 0425.20038Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 2 1979 Dieudonné’s hypothesis on the structure of unitary groups over a skew field and Hermitian K-theory. Zbl 0579.16011Platonov, V. P.; Yanchevskij, V. I. 2 1984 Addendum to the paper ”The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups”. Zbl 0236.20034Platonov, V. P. 2 1971 On the genus problem in arithmetic groups. Zbl 0256.20059Platonov, V. P. 2 1971 Algebraische d-Gruppen. Zbl 0274.20059Platonov, V. P. 2 1963 The reduced Whitehead group for cyclic algebras. Zbl 0345.16023Platonov, V. P. 2 1976 Dieudonne’s conjecture and the nonsurjectivity on k-points of coverings of algebraic groups. Zbl 0348.20040Platonov, V. P. 2 1974 On the infiniteness of the reduced Whitehead group. Zbl 0362.16009Platonov, V. P. 2 1976 Grothendieck’s problem on profinite completions and representations of groups. Zbl 0722.20020Platonov, V. P.; Tavgen’, O. I. 2 1990 Rigidity and automorphism groups of solvable arithmetic groups. Zbl 0914.20043Grunewald, Fritz; Platonov, Vladimir 2 1998 Automorphisms of algebraic groups. Zbl 0158.27802Platonov, V. P. 2 1966 Proof of the finiteness hypothesis for the solvable subgroups of algebraic groups. Zbl 0196.05203Platonov, V. P. 2 1970 Splittable linear groups. Zbl 0227.20016Platonov, V. P. 2 1963 New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order. Zbl 1356.11038Platonov, V. P.; Petrunin, M. M. 2 2015 Arithmetic properties of quadratic function fields and torsion in Jacobians. Zbl 1320.11106Platonov, V. P. 2 2010 Adelic profinite groups. Zbl 0884.20018Platonov, V. P.; Sury, B. 2 1997 The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. Zbl 1439.11286Platonov, Vladimir Petrovich; Fedorov, Gleb Vladimirovich 1 2019 Birational properties of spinor varieties. Zbl 0522.14004Platonov, V. P. 1 1983 Dieudonné’s conjecture on the structure of unitary groups, and division rings over Henselian fields. Zbl 0595.16017Platonov, V. P.; Yanchevskij, V. I. 1 1984 On the classification problem for polynomials \(f\) with a periodic continued fraction expansion of \(\sqrt{f}\) in hyperelliptic fields. Zbl 1483.11123Platonov, V. P.; Fedorov, G. V. 1 2021 On the problem of classification of periodic continued fractions in hyperelliptic fields. Zbl 1451.11127Platonov, V. P.; Fedorov, G. V. 5 2020 On the finiteness of the number of expansions into a continued fraction of \( \sqrt f\) for cubic polynomials over algebraic number fields. Zbl 1479.11202Platonov, V. P.; Petrunin, M. M. 1 2020 On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\). Zbl 1477.11187Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N. 8 2019 The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. Zbl 1439.11286Platonov, Vladimir Petrovich; Fedorov, Gleb Vladimirovich 1 2019 On \(S\)-units for linear valuations and the periodicity of continued fractions of generalized type in hyperelliptic fields. Zbl 1439.11164Platonov, V. P.; Fedorov, G. V. 1 2019 On infinite-dimensional integer Hankel matrices. Zbl 1419.15027Platonov, V. P.; Petrunin, M. M. 1 2019 On the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1445.11135Platonov, V. P.; Fedorov, G. V. 19 2018 Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1440.11127Platonov, V. P.; Petrunin, M. M. 13 2018 On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\). Zbl 1428.11131Platonov, V. P.; Zhgoon, V. S.; Petrunin, M. M.; Shteinikov, Yu. N. 7 2018 On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field. Zbl 1443.11141Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V. 6 2018 An infinite family of curves of genus 2 over the field of rational numbers whose Jacobian varieties contain rational points of order 28. Zbl 1427.14062Platonov, V. P.; Fedorov, G. V. 3 2018 On new arithmetic properties of determinants of Hankel matrices. Zbl 1400.15012Platonov, V. P.; Petrunin, M. M. 2 2018 On the periodicity of continued fractions in hyperelliptic fields. Zbl 1418.11109Platonov, V. P.; Fedorov, G. V. 13 2017 On the periodicity of continued fractions in elliptic fields. Zbl 1392.11048Platonov, V. P.; Fedorov, G. V. 11 2017 On new properties of Hankel matrices over the field of rational numbers. Zbl 1432.11031Platonov, Vladimir P. 3 2017 Continued rational fractions in hyperelliptic fields and the Mumford representation. Zbl 1403.11071Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V. 13 2016 \(S\)-units in hyperelliptic fields and periodicity of continued fractions. Zbl 1392.11035Platonov, V. P.; Petrunin, M. M. 13 2016 \(S\)-units and periodicity in quadratic function fields. Zbl 1357.11111Platonov, V. P.; Petrunin, M. M. 13 2016 \(S\)-units and periodicity of continued fractions in hyperelliptic fields. Zbl 1337.11040Platonov, V. P.; Fedorov, G. V. 14 2015 Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves. Zbl 1348.14083Platonov, V. P.; Petrunin, M. M. 6 2015 New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order. Zbl 1356.11038Platonov, V. P.; Petrunin, M. M. 2 2015 Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field. Zbl 1305.11096Platonov, V. P. 36 2014 On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order. Zbl 1278.14045Platonov, V. P.; Zhgun, V. S.; Petrunin, M. M. 5 2013 New orders of torsion points in Jacobians of curves of genus 2 over the rational number field. Zbl 1319.11041Platonov, V. P.; Petrunin, M. M. 10 2012 Arithmetic of quadratic fields and torsion in Jacobians. Zbl 1217.11094Platonov, V. P. 10 2010 A new local-global principle for quadratic function fields. Zbl 1244.11093Benyash-Krivets, V. V.; Platonov, V. P. 5 2010 Arithmetic properties of quadratic function fields and torsion in Jacobians. Zbl 1320.11106Platonov, V. P. 2 2010 New properties of arithmetic groups. Zbl 1214.20045Platonov, V. P. 1 2010 Groups of \(S\)-units in hyperelliptic fields and continued fractions. Zbl 1231.11131Benyash-Krivets, V. V.; Platonov, V. P. 22 2009 Continued fractions and \(S\)-units in hyperelliptic fields. Zbl 1225.11160Benyash-Krivets, V. V.; Platonov, V. P. 3 2008 Continued fractions and \(S\)-units in function fields. Zbl 1221.11224Benyash-Krivets, V. V.; Platonov, V. P. 1 2008 Groups of \(S\)-units in hyperelliptic fields. Zbl 1154.11039Benyash-Krivets, V. V.; Platonov, V. P. 3 2007 \(S\)-units in hyperelliptic fields. Zbl 1176.11053Benyash-Krivets, V. V.; Platonov, V. P. 1 2007 On the linearity of automorphism groups for free metabelian groups. Zbl 1155.20310Platonov, V. P. 1 2006 New combinatorial properties of linear groups. Zbl 0983.20041Platonov, Vladimir P.; Potapchik, Alexander 3 2001 Rigidity results for groups with radical cohomology of finite groups and arithmeticity problems. Zbl 1007.11029Grunewald, Fritz; Platonov, Vladimir 6 1999 Solvable arithmetic groups and arithmeticity problems. Zbl 1039.20026Grunewald, Fritz; Platonov, Vladimir 4 1999 Rigidity for groups with radical, cohomology of finite groups, and arithmeticity problems. Zbl 0941.20052Platonov, V. P. 1 1999 The rationality problem for semisimple group varieties. Zbl 0904.20036Chernousov, Vladimir I.; Platonov, Vladimir P. 8 1998 Non-arithmetic polycyclic groups. Zbl 0974.20035Grunewald, Fritz; Platonov, Vladimir 3 1998 Rigidity and automorphism groups of solvable arithmetic groups. Zbl 0914.20043Grunewald, Fritz; Platonov, Vladimir 2 1998 On finite extensions of arithmetic groups. Zbl 0913.20034Grunewald, Fritz; Platonov, Vladimir 6 1997 Adelic profinite groups. Zbl 0884.20018Platonov, V. P.; Sury, B. 2 1997 Subgroups of \(\text{GL}(n^ 2,\mathbf C)\) containing \(\text{PSU}(n)\). Zbl 0848.20033Platonov, V. P.; Đoković, D. Ž. 6 1996 Low-dimensional representations of \(\text{Aut}(F_ 2)\). Zbl 0862.20006Đoković, Dragomir Ž.; Platonov, Vladimir P. 5 1996 Linear preserver problems and algebraic groups. Zbl 0836.20065Platonov, Vladimir P.; Đoković, Dragomir Ž. 13 1995 Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046Platonov, Vladimir; Rapinchuk, Andrei 279 1994 Subgroups of algebraic groups over a local or global field containing a maximal torus. Zbl 0831.20062Platonov, Vladimir P. 3 1994 Algebraic groups and linear preserver problems. Zbl 0811.20044Đoković, Dragomir Ž.; Platonov, Vladimir P. 6 1993 Algebraic groups and number theory. Zbl 0806.11002Platonov, V. P.; Rapinchuk, A. S. 109 1992 Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025Platonov, V. P.; Rapinchuk, A. S. 12 1992 Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027Platonov, V. P.; Rapinchuk, A. S. 49 1991 Character rings of representations of finitely generated groups. Zbl 0766.20008Platonov, V. P.; Benyash-Krivets, V. V. 5 1990 Grothendieck’s problem on profinite completions and representations of groups. Zbl 0722.20020Platonov, V. P.; Tavgen’, O. I. 2 1990 Rings and varieties of representations of finitely generated groups. Zbl 0765.20011Platonov, V. P. 5 1989 Finite-dimensional Henselian division algebras. Zbl 0669.16016Platonov, V. P.; Yanchevskij, V. I. 3 1988 On the theory of Henselian division algebras. Zbl 0667.16018Platonov, V. P.; Yanchevskij, V. I. 2 1988 The Hasse norm principle for algebraic number fields. Zbl 0624.12009Drakokhrust, Yu. A.; Platonov, V. P. 8 1987 Character rings of \(n\)-dimensional representations of finitely generated groups. Zbl 0669.20004Platonov, V. P.; Benyash-Krivets, V. V. 1 1987 On Grothendieck’s problem on profinite completions of groups. Zbl 0614.20016Platonov, V. P.; Tavgen’, O. I. 6 1986 Dieudonné’s conjecture on the structure of unitary groups over a division ring, and Hermitian K-theory. Zbl 0593.16012Platonov, V. P.; Yanchevskij, V. I. 4 1985 On the Hasse principle for algebraic number fields. Zbl 0604.12011Platonov, V. P.; Drakokhrust, Yu. A. 1 1985 The Hasse norm principle for primary extensions of algebraic number fields. Zbl 0604.12012Platonov, V. P.; Drakokhrust, Yu. A. 1 1985 The multiplicative structure of division rings over number fields and the Hasse norm principle. Zbl 0579.12010Platonov, V. P.; Rapinchuk, A. S. 1 1985 Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010Platonov, V. P.; Rapinchuk, A. S. 4 1984 Dieudonné’s hypothesis on the structure of unitary groups over a skew field and Hermitian K-theory. Zbl 0579.16011Platonov, V. P.; Yanchevskij, V. I. 2 1984 Dieudonné’s conjecture on the structure of unitary groups, and division rings over Henselian fields. Zbl 0595.16017Platonov, V. P.; Yanchevskij, V. I. 1 1984 Algebraic groups. Zbl 0564.20023Platonov, V. P.; Rapinchuk, A. S. 2 1983 Birational properties of spinor varieties. Zbl 0522.14004Platonov, V. P. 1 1983 Arithmetic theory of algebraic groups. Zbl 0502.20025Platonov, V. P. 11 1982 The arithmetic theory of algebraic groups. Zbl 0513.20028Platonov, V. P. 3 1982 The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029Platonov, V. P.; Rapinchuk, A. S. 3 1982 Birational properties of spinor varieties. Zbl 0496.14008Platonov, V. P. 3 1981 Class numbers and groups of algebraic groups. II. Zbl 0464.20031Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1981 Algebraic groups and reduced K-theory. Zbl 0425.16018Platonov, V. P. 6 1980 On the rationality of canonical spinor varieties. Zbl 0486.14013Platonov, V. P.; Chernousov, V. I. 4 1980 Class numbers and groups of algebraic groups. Zbl 0448.20045Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 1 1980 On the group of rational points of three-dimensional groups. Zbl 0431.12012Platonov, V. P.; Rapinchuk, A. S. 7 1979 Class number of algebraic groups. Zbl 0425.20038Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S. 2 1979 Correction. Zbl 0419.16013Platonov, V. P.; Yanchevskij, V. I. 1 1979 On the problem of rationality of spinor varieties. Zbl 0435.20028Platonov, V. P. 1 1979 On reduced K-theory for n-fold Hensel fields. Zbl 0436.13008Platonov, V. P. 1 1979 The Tannaka-Artin problem and reduced K-theory. Zbl 0349.16008Platonov, V. P. 12 1977 Birational properties of the reduced Whitehead group. Zbl 0791.20045Platonov, V. P. 3 1977 Das Tannaka-Artinsche Problem und reduzierte K-Theorie. Zbl 0338.16005Platonov, V. P. 12 1976 Die Unendlichkeit der reduzierten Whiteheadgruppe im Tannaka-Artin- Problem. Zbl 0352.16009Platonov, V. P. 5 1976 Reduced K-theory and approximation in algebraic groups. Zbl 0417.16012Platonov, V. P. 2 1976 The reduced Whitehead group for cyclic algebras. Zbl 0345.16023Platonov, V. P. 2 1976 On the infiniteness of the reduced Whitehead group. Zbl 0362.16009Platonov, V. P. 2 1976 Bemerkungen zu meiner Arbeit ”Das Tannaka-Artin Problem und reduzierte K- Theorie”. Zbl 0343.16014Platonov, V. P. 1 1976 On the Tannaka-Artin problem. Zbl 0333.20032Platonov, V. P. 11 1975 On Harder’s conjecture. Zbl 0333.20035Platonov, V. P.; Yanchevskii, V. I. 4 1975 A problem of Tannaka-Artin and groups of projective conorms. Zbl 0338.16004Platonov, V. P. 4 1975 On the Kneser-Tits conjecture for unitary groups. Zbl 0343.16016Platonov, V. P.; Yanchevskii, V. I. 3 1975 The arithmetic theory of linear algebraic groups and number theory. Zbl 0305.20023Platonov, V. P. 1 1975 Dieudonne’s conjecture and the nonsurjectivity on k-points of coverings of algebraic groups. Zbl 0348.20040Platonov, V. P. 2 1974 Determination of algebraic groups by arithmetic subgroups. Zbl 0312.20024Platonov, V. P.; Milovanov, M. V. 6 1973 The structure of unitary groups and the commutator group of a simple algebra over global fields. Zbl 0298.20035Platonov, V. P.; Yanchevskii, V. I. 5 1973 ...and 31 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 663 Authors 38 Platonov, Vladimir Petrovich 28 Rapinchuk, Andrei S. 18 Petrunin, Maksim Maksimovich 17 Fëdorov, Gleb Vladimirovich 16 Lubotzky, Alexander 14 Chernousov, Vladimir I. 13 Grunewald, Fritz J. 11 Nguyễn Quôc Thăng 9 Prasad, Gopal 8 Einsiedler, Manfred Leopold 8 Rapinchuk, Igor A. 7 Hazrat, Roozbeh 7 Kunyavskiĭ, Boris Èmmanuilovich 7 Margulis, Grigoriĭ Aleksandrovich 7 Parimala, Raman 7 Witte Morris, Dave 7 Zhgoon, Vladimir S. 6 Belolipetsky, Mikhail V. 6 Benyash-Krivets, Valeriĭ Vatslavovich 6 Borovoi, Mikhail V. 6 Gelander, Tsachik 6 Gordeev, Nikolai L. 6 Guralnick, Robert Michael 6 Kaletha, Tasho 6 Oh, Hee 6 Shteĭnikov, Yuriĭ Nikolaevich 6 Yanchevskii, Vyacheslav Ivanovich 5 Avni, Nir 5 Bridson, Martin R. 5 Caprace, Pierre-Emmanuel 5 Garibaldi, Skip 5 Gille, Philippe 5 Li, Chi-Kwong 5 Sarnak, Peter Clive 5 Segev, Yoav 5 Stern, Leonid 5 Venkataramana, Tyakal Nanjundiah 5 Wesolek, Phillip Richard 5 Zalesskii, Pavel 4 Aka, Menny 4 Arenas-Carmona, Luis 4 Bader, Uri 4 Bitan, Rony A. 4 Bukhshtaber, Viktor Matveevich 4 Cao, Yang 4 Choiy, Kwangho 4 Đoković, Dragomir Ž. 4 Draper, Cristina 4 Gorodnik, Alexander 4 Larsen, Michael Jeffrey 4 Martín González, Cándido 4 McReynolds, David Ben 4 Merkur’ev, Aleksandr Sergeevich 4 Raghunathan, Madabusi Santanam 4 Segal, Daniel 4 Stover, Matthew 4 Sury, Balasubramanian 4 Thakur, Maneesh L. 4 Vavilov, Nikolaĭ Aleksandrovich 4 Venkatesh, Akshay 4 Wadsworth, Adrian R. 4 Wei, Dasheng 4 Wortman, Kevin A. 4 Yafaev, Andrei 4 Zalesski, Alexandre Efimovich 3 Bou-Rabee, Khalid 3 Calderón Martín, Antonio Jesús 3 Chan, Wai Kiu 3 Colliot-Thélène, Jean-Louis 3 Fiori, Andrew 3 Flicker, Yuval Z. 3 Gao, Ziyang 3 Gefter, Sergey L. 3 Glasner, Yair 3 Hooda, Neha 3 Jaikin-Zapirain, Andrei 3 Kammeyer, Holger 3 Kim, Henry H. 3 Klopsch, Benjamin 3 Koibaev, Vladimir Amurkhanovich 3 Liebeck, Martin Walter 3 Lim, Seonhee 3 Linowitz, Benjamin 3 Mazur, Marcin 3 Merzlyakov, Yu. I. 3 Mohammadi, Amir 3 Monod, Nicolas 3 Mozes, Shahar 3 Mukhin, Yurii N. 3 Omladič, Matjaž 3 Onn, Uri 3 Pillay, Anand 3 Potapchik, Alexander 3 Rehmann, Ulf 3 Reid, Alan W. 3 Rohlfs, Jürgen 3 Samuels, Beth 3 Sauer, Roman 3 Šemrl, Peter 3 Shapira, Uri ...and 563 more Authors all top 5 Cited in 139 Serials 66 Journal of Algebra 30 Doklady Mathematics 29 Duke Mathematical Journal 27 Transactions of the American Mathematical Society 25 Journal of Number Theory 23 Mathematische Zeitschrift 22 Israel Journal of Mathematics 20 Inventiones Mathematicae 16 Proceedings of the American Mathematical Society 16 Journal of Mathematical Sciences (New York) 15 Advances in Mathematics 13 Geometriae Dedicata 13 Journal of Soviet Mathematics 12 Mathematical Notes 12 Mathematische Annalen 11 Journal of the American Mathematical Society 10 Communications in Algebra 10 Annales de l’Institut Fourier 10 Compositio Mathematica 10 Linear Algebra and its Applications 10 Chebyshevskiĭ Sbornik 9 Publications Mathématiques 9 Manuscripta Mathematica 9 Annals of Mathematics. Second Series 8 Ukrainian Mathematical Journal 8 Siberian Mathematical Journal 8 Journal of the European Mathematical Society (JEMS) 8 Forum of Mathematics, Sigma 7 Michigan Mathematical Journal 7 Geometric and Functional Analysis. GAFA 7 Proceedings of the Steklov Institute of Mathematics 7 Algebra & Number Theory 6 Journal für die Reine und Angewandte Mathematik 6 International Journal of Number Theory 5 Linear and Multilinear Algebra 5 Journal of Pure and Applied Algebra 5 Memoirs of the American Mathematical Society 5 Ergodic Theory and Dynamical Systems 5 Bulletin of the American Mathematical Society. New Series 5 Documenta Mathematica 5 Representation Theory 5 Geometry & Topology 4 Journal d’Analyse Mathématique 4 Nagoya Mathematical Journal 4 \(K\)-Theory 4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences 4 Comptes Rendus. Mathématique. Académie des Sciences, Paris 4 Journal of the Institute of Mathematics of Jussieu 3 Mathematical Proceedings of the Cambridge Philosophical Society 3 Russian Mathematical Surveys 3 Algebra and Logic 3 Archiv der Mathematik 3 Pacific Journal of Mathematics 3 Proceedings of the London Mathematical Society. Third Series 3 Annals of Pure and Applied Logic 3 Forum Mathematicum 3 International Journal of Mathematics 3 International Journal of Algebra and Computation 3 Algebraic & Geometric Topology 3 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications 3 Groups, Geometry, and Dynamics 2 Communications in Mathematical Physics 2 Mathematics of Computation 2 Abhandlungen aus dem Mathematischen Seminar der Universität Hamburg 2 Acta Arithmetica 2 Annales Scientifiques de l’École Normale Supérieure. Quatrième Série 2 Commentarii Mathematici Helvetici 2 Journal of Functional Analysis 2 Journal of the London Mathematical Society. Second Series 2 Journal of the Mathematical Society of Japan 2 Monatshefte für Mathematik 2 Publications of the Research Institute for Mathematical Sciences, Kyoto University 2 Journal de Théorie des Nombres de Bordeaux 2 St. Petersburg Mathematical Journal 2 Bulletin des Sciences Mathématiques 2 Transformation Groups 2 Journal of Group Theory 2 Trudy Instituta Matematiki 2 Journal of Modern Dynamics 2 Journal of \(K\)-Theory 1 Bulletin of the Australian Mathematical Society 1 Communications on Pure and Applied Mathematics 1 Journal of Mathematical Physics 1 Journal of Geometry and Physics 1 Acta Mathematica 1 Biometrical Journal 1 Bulletin of the London Mathematical Society 1 Bulletin de la Société Mathématique de France 1 Functiones et Approximatio. Commentarii Mathematici 1 Functional Analysis and its Applications 1 Fundamenta Mathematicae 1 Indiana University Mathematics Journal 1 The Journal of Symbolic Logic 1 Kodai Mathematical Journal 1 Mathematika 1 Proceedings of the Japan Academy. Series A 1 Rendiconti del Circolo Matemàtico di Palermo. Serie II 1 Transactions of the Moscow Mathematical Society 1 Topology and its Applications 1 European Journal of Combinatorics ...and 39 more Serials all top 5 Cited in 41 Fields 338 Number theory (11-XX) 314 Group theory and generalizations (20-XX) 184 Topological groups, Lie groups (22-XX) 161 Algebraic geometry (14-XX) 65 Associative rings and algebras (16-XX) 38 Field theory and polynomials (12-XX) 37 Dynamical systems and ergodic theory (37-XX) 34 Manifolds and cell complexes (57-XX) 30 Nonassociative rings and algebras (17-XX) 24 Linear and multilinear algebra; matrix theory (15-XX) 24 Differential geometry (53-XX) 22 \(K\)-theory (19-XX) 14 Combinatorics (05-XX) 13 Several complex variables and analytic spaces (32-XX) 13 Geometry (51-XX) 12 Category theory; homological algebra (18-XX) 11 Mathematical logic and foundations (03-XX) 10 Global analysis, analysis on manifolds (58-XX) 7 Measure and integration (28-XX) 6 Abstract harmonic analysis (43-XX) 6 Operator theory (47-XX) 6 Algebraic topology (55-XX) 5 Functional analysis (46-XX) 4 History and biography (01-XX) 4 Commutative algebra (13-XX) 4 Functions of a complex variable (30-XX) 3 Convex and discrete geometry (52-XX) 2 Special functions (33-XX) 2 General topology (54-XX) 2 Probability theory and stochastic processes (60-XX) 2 Computer science (68-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 2 Information and communication theory, circuits (94-XX) 1 Order, lattices, ordered algebraic structures (06-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 Statistics (62-XX) 1 Biology and other natural sciences (92-XX) Citations by Year Wikidata Timeline The data are displayed as stored in Wikidata under a Creative Commons CC0 License. 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