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Platonov, Vladimir Petrovich

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Author ID: platonov.vladimir-p Recent zbMATH articles by "Platonov, Vladimir Petrovich"
Published as: Platonov, V. P.; Platonov, Vladimir Petrovich; Platonov, Vladimir P.; Platonov, Vladimir; Platonov, V.
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Documents Indexed: 185 Publications since 1962, including 3 Books
Biographic References: 8 Publications
all top 5

Co-Authors

88 single-authored
16 Rapinchuk, Andrei S.
14 Petrunin, Maksim Maksimovich
13 Yanchevskii, Vyacheslav Ivanovich
10 Fëdorov, Gleb Vladimirovich
8 Benyash-Krivets, Valeriĭ Vatslavovich
6 Grunewald, Fritz J.
4 Bondarenko, Aleksandr Adamovich
4 Chernousov, Vladimir I.
4 Đoković, Dragomir Ž.
4 Parshin, Alexei N.
4 Zhgoon, Vladimir S.
3 Drakokhrust, Yu. A.
3 Shteĭnikov, Yuriĭ Nikolaevich
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 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 Konjuh, 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

Publications by Year

Citations contained in zbMATH Open

127 Publications have been cited 982 times in 657 Documents Cited by Year
Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046
Platonov, Vladimir; Rapinchuk, Andrei
254
1994
Algebraic groups and number theory. Zbl 0806.11002
Platonov, V. P.; Rapinchuk, A. S.
101
1992
Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027
Platonov, V. P.; Rapinchuk, A. S.
45
1991
Number-theoretic properties of hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves over the rational number field. Zbl 1305.11096
Platonov, V. P.
32
2014
Groups of \(S\)-units in hyperelliptic fields and continued fractions. Zbl 1231.11131
Benyash-Krivets, V. V.; Platonov, V. P.
22
2009
The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups. Zbl 0217.36301
Platonov, V. P.
18
1971
On the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1445.11135
Platonov, V. P.; Fedorov, G. V.
16
2018
\(S\)-units and periodicity of continued fractions in hyperelliptic fields. Zbl 1337.11040
Platonov, V. P.; Fedorov, G. V.
14
2015
Linear preserver problems and algebraic groups. Zbl 0836.20065
Platonov, Vladimir P.; Đoković, Dragomir Ž.
13
1995
Locally projectively nilpotent subgroups and nilelements in topological groups. Zbl 0222.22002
Platonov, V. P.
13
1966
\(S\)-units in hyperelliptic fields and periodicity of continued fractions. Zbl 1392.11035
Platonov, V. P.; Petrunin, M. M.
13
2016
Continued rational fractions in hyperelliptic fields and the Mumford representation. Zbl 1403.11071
Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V.
13
2016
\(S\)-units and periodicity in quadratic function fields. Zbl 1357.11111
Platonov, V. P.; Petrunin, M. M.
13
2016
Das Tannaka-Artinsche Problem und reduzierte K-Theorie. Zbl 0338.16005
Platonov, V. P.
12
1976
The Tannaka-Artin problem and reduced K-theory. Zbl 0349.16008
Platonov, V. P.
12
1977
On the periodicity of continued fractions in hyperelliptic fields. Zbl 1418.11109
Platonov, V. P.; Fedorov, G. V.
12
2017
On the periodicity of continued fractions in elliptic fields. Zbl 1392.11048
Platonov, V. P.; Fedorov, G. V.
11
2017
Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1440.11127
Platonov, V. P.; Petrunin, M. M.
11
2018
Arithmetic theory of algebraic groups. Zbl 0502.20025
Platonov, V. P.
10
1982
Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025
Platonov, V. P.; Rapinchuk, A. S.
10
1992
New orders of torsion points in Jacobians of curves of genus 2 over the rational number field. Zbl 1319.11041
Platonov, V. P.; Petrunin, M. M.
10
2012
On the Tannaka-Artin problem. Zbl 0333.20032
Platonov, V. P.
10
1975
Arithmetic of quadratic fields and torsion in Jacobians. Zbl 1217.11094
Platonov, V. P.
10
2010
Engel elements and the radical in PI-algebras and topological groups. Zbl 0136.29503
Platonov, V. P.
8
1965
The rationality problem for semisimple group varieties. Zbl 0904.20036
Chernousov, Vladimir I.; Platonov, Vladimir P.
7
1998
On the group of rational points of three-dimensional groups. Zbl 0431.12012
Platonov, V. P.; Rapinchuk, A. S.
7
1979
Theory of algebraic linear groups and periodic groups. Zbl 0177.04802
Platonov, V. P.
7
1968
Subgroups of \(\text{GL}(n^ 2,\mathbf C)\) containing \(\text{PSU}(n)\). Zbl 0848.20033
Platonov, V. P.; Đoković, D. Ž.
6
1996
Algebraic groups and linear preserver problems. Zbl 0811.20044
Đoković, Dragomir Ž.; Platonov, Vladimir P.
6
1993
Rigidity results for groups with radical cohomology of finite groups and arithmeticity problems. Zbl 1007.11029
Grunewald, Fritz; Platonov, Vladimir
6
1999
On finite extensions of arithmetic groups. Zbl 0913.20034
Grunewald, Fritz; Platonov, Vladimir
6
1997
Algebraic groups and reduced K-theory. Zbl 0425.16018
Platonov, V. P.
6
1980
A proof of the finiteness hypothesis for solvable subgroups of algebraic groups. (Beweis der Endlichkeitshypothese für auflösbare Untergruppen algebraischer Gruppen.) Zbl 0182.04702
Platonov, V. P.
6
1969
A certain problem for finitely generated groups. Zbl 0228.20018
Platonov, V. P.
6
1968
Determination of algebraic groups by arithmetic subgroups. Zbl 0312.20024
Platonov, V. P.; Milovanov, M. V.
6
1973
Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves. Zbl 1348.14083
Platonov, V. P.; Petrunin, M. M.
6
2015
On Grothendieck’s problem on profinite completions of groups. Zbl 0614.20016
Platonov, V. P.; Tavgen’, O. I.
6
1986
The Hasse norm principle for algebraic number fields. Zbl 0624.12009
Drakokhrust, Yu. A.; Platonov, V. P.
6
1987
On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\). Zbl 1428.11131
Platonov, V. P.; Zhgoon, V. S.; Petrunin, M. M.; Shteinikov, Yu. N.
6
2018
On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\). Zbl 07179390
Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N.
6
2019
Rings and varieties of representations of finitely generated groups. Zbl 0765.20011
Platonov, V. P.
5
1989
Character rings of representations of finitely generated groups. Zbl 0766.20008
Platonov, V. P.; Benyash-Krivets, V. V.
5
1990
Low-dimensional representations of \(\text{Aut}(F_ 2)\). Zbl 0862.20006
Đoković, Dragomir Ž.; Platonov, Vladimir P.
5
1996
On the simplicity of Jacobians for hyperelliptic curves of genus 2 over the field of rational numbers with torsion points of high order. Zbl 1278.14045
Platonov, V. P.; Zhgun, V. S.; Petrunin, M. M.
5
2013
The Frattini subgroup of linear groups and finite approximability. Zbl 0242.20038
Platonov, V. P.
5
1966
Lokal projective nilpotent radicals in topological groups. Zbl 0242.22006
Platonov, V. P.
5
1965
The structure of unitary groups and the commutator group of a simple algebra over global fields. Zbl 0298.20035
Platonov, V. P.; Yanchevskii, V. I.
5
1973
Die Unendlichkeit der reduzierten Whiteheadgruppe im Tannaka-Artin- Problem. Zbl 0352.16009
Platonov, V. P.
5
1976
A new local-global principle for quadratic function fields. Zbl 1244.11093
Benyash-Krivets, V. V.; Platonov, V. P.
5
2010
On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field. Zbl 1443.11141
Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V.
5
2018
Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010
Platonov, V. P.; Rapinchuk, A. S.
4
1984
On the rationality of canonical spinor varieties. Zbl 0486.14013
Platonov, V. P.; Chernousov, V. I.
4
1980
On Harder’s conjecture. Zbl 0333.20035
Platonov, V. P.; Yanchevskii, V. I.
4
1975
A problem of Tannaka-Artin and groups of projective conorms. Zbl 0338.16004
Platonov, V. P.
4
1975
Dieudonné’s conjecture on the structure of unitary groups over a division ring, and Hermitian K-theory. Zbl 0593.16012
Platonov, V. P.; Yanchevskij, V. I.
4
1985
Solvable arithmetic groups and arithmeticity problems. Zbl 1039.20026
Grunewald, Fritz; Platonov, Vladimir
3
1999
Birational properties of spinor varieties. Zbl 0496.14008
Platonov, V. P.
3
1981
The arithmetic theory of algebraic groups. Zbl 0513.20028
Platonov, V. P.
3
1982
The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029
Platonov, V. P.; Rapinchuk, A. S.
3
1982
Finite-dimensional Henselian division algebras. Zbl 0669.16016
Platonov, V. P.; Yanchevskij, V. I.
3
1988
Birational properties of the reduced Whitehead group. Zbl 0791.20045
Platonov, V. P.
3
1977
Subgroups of algebraic groups over a local or global field containing a maximal torus. Zbl 0831.20062
Platonov, Vladimir P.
3
1994
Certain classes of topological groups. Zbl 0166.02701
Platonov, V. P.
3
1966
The structure of periodic linear groups and algebraic groups. Zbl 0171.28802
Platonov, V. P.
3
1966
On Auerbach’s problem. Zbl 0225.20025
Platonov, V. P.; Zalesskij, A. E.
3
1966
On the maximality problem for arithmetic groups. Zbl 0252.20050
Platonov, V. P.
3
1971
On the Kneser-Tits conjecture for unitary groups. Zbl 0343.16016
Platonov, V. P.; Yanchevskii, V. I.
3
1975
On new properties of Hankel matrices over the field of rational numbers. Zbl 1432.11031
Platonov, Vladimir P.
3
2017
On the problem of classification of periodic continued fractions in hyperelliptic fields. Zbl 1451.11127
Platonov, V. P.; Fedorov, G. V.
3
2020
Groups of \(S\)-units in hyperelliptic fields. Zbl 1154.11039
Benyash-Krivets, V. V.; Platonov, V. P.
3
2007
Continued fractions and \(S\)-units in hyperelliptic fields. Zbl 1225.11160
Benyash-Krivets, V. V.; Platonov, V. P.
3
2008
Some remarks on linear groups. Zbl 0215.39701
Platonov, V. P.
3
1968
An infinite family of curves of genus 2 over the field of rational numbers whose Jacobian varieties contain rational points of order 28. Zbl 1427.14062
Platonov, V. P.; Fedorov, G. V.
3
2018
New combinatorial properties of linear groups. Zbl 0983.20041
Platonov, Vladimir P.; Potapchik, Alexander
2
2001
Algebraic groups. Zbl 0564.20023
Platonov, V. P.; Rapinchuk, A. S.
2
1983
On the theory of Henselian division algebras. Zbl 0667.16018
Platonov, V. P.; Yanchevskij, V. I.
2
1988
Adelic profinite groups. Zbl 0884.20018
Platonov, V. P.; Sury, B.
2
1997
Non-arithmetic polycyclic groups. Zbl 0974.20035
Grunewald, Fritz; Platonov, Vladimir
2
1998
Rigidity and automorphism groups of solvable arithmetic groups. Zbl 0914.20043
Grunewald, Fritz; Platonov, Vladimir
2
1998
Reduced K-theory and approximation in algebraic groups. Zbl 0417.16012
Platonov, V. P.
2
1976
Class number of algebraic groups. Zbl 0425.20038
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
2
1979
Structure of topological locally projectively nilpotent groups, and of groups with a normalizer condition. Zbl 0164.34203
Platonov, V. P.
2
1968
Proof of the finiteness hypothesis for the solvable subgroups of algebraic groups. Zbl 0196.05203
Platonov, V. P.
2
1970
New curves of genus 2 over the field of rational numbers whose Jacobians contain torsion points of high order. Zbl 1356.11038
Platonov, V. P.; Petrunin, M. M.
2
2015
Splittable linear groups. Zbl 0227.20016
Platonov, V. P.
2
1963
Addendum to the paper ”The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups”. Zbl 0236.20034
Platonov, V. P.
2
1971
On the genus problem in arithmetic groups. Zbl 0256.20059
Platonov, V. P.
2
1971
Algebraische d-Gruppen. Zbl 0274.20059
Platonov, V. P.
2
1963
The reduced Whitehead group for cyclic algebras. Zbl 0345.16023
Platonov, V. P.
2
1976
Dieudonne’s conjecture and the nonsurjectivity on k-points of coverings of algebraic groups. Zbl 0348.20040
Platonov, V. P.
2
1974
On the infiniteness of the reduced Whitehead group. Zbl 0362.16009
Platonov, V. P.
2
1976
Dieudonné’s hypothesis on the structure of unitary groups over a skew field and Hermitian K-theory. Zbl 0579.16011
Platonov, V. P.; Yanchevskij, V. I.
2
1984
On new arithmetic properties of determinants of Hankel matrices. Zbl 1400.15012
Platonov, V. P.; Petrunin, M. M.
2
2018
Automorphisms of algebraic groups. Zbl 0158.27802
Platonov, V. P.
2
1966
Arithmetic properties of quadratic function fields and torsion in Jacobians. Zbl 1320.11106
Platonov, V. P.
2
2010
Birational properties of spinor varieties. Zbl 0522.14004
Platonov, V. P.
1
1983
Character rings of \(n\)-dimensional representations of finitely generated groups. Zbl 0669.20004
Platonov, V. P.; Benyash-Krivets, V. V.
1
1987
On the congruence problem for linear groups over arithmetic rings. Zbl 0791.20052
Platonov, V. P.; Sharomet, A. A.
1
1972
Rigidity for groups with radical, cohomology of finite groups, and arithmeticity problems. Zbl 0941.20052
Platonov, V. P.
1
1999
Correction. Zbl 0419.16013
Platonov, V. P.; Yanchevskij, V. I.
1
1979
On the problem of classification of periodic continued fractions in hyperelliptic fields. Zbl 1451.11127
Platonov, V. P.; Fedorov, G. V.
3
2020
On the finiteness of the number of elliptic fields with given degrees of \(S\)-units and periodic expansion of \( \sqrt f\). Zbl 07179390
Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N.
6
2019
On infinite-dimensional integer Hankel matrices. Zbl 1419.15027
Platonov, V. P.; Petrunin, M. M.
1
2019
The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. Zbl 1439.11286
Platonov, 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 1439.11164
Platonov, V. P.; Fedorov, G. V.
1
2019
On the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1445.11135
Platonov, V. P.; Fedorov, G. V.
16
2018
Groups of \(S\)-units and the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1440.11127
Platonov, V. P.; Petrunin, M. M.
11
2018
On the finiteness of hyperelliptic fields with special properties and periodic expansion of \(\sqrt{f}\). Zbl 1428.11131
Platonov, V. P.; Zhgoon, V. S.; Petrunin, M. M.; Shteinikov, Yu. N.
6
2018
On the periodicity of continued fractions in hyperelliptic fields over quadratic constant field. Zbl 1443.11141
Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V.
5
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 1427.14062
Platonov, V. P.; Fedorov, G. V.
3
2018
On new arithmetic properties of determinants of Hankel matrices. Zbl 1400.15012
Platonov, V. P.; Petrunin, M. M.
2
2018
On the periodicity of continued fractions in hyperelliptic fields. Zbl 1418.11109
Platonov, V. P.; Fedorov, G. V.
12
2017
On the periodicity of continued fractions in elliptic fields. Zbl 1392.11048
Platonov, V. P.; Fedorov, G. V.
11
2017
On new properties of Hankel matrices over the field of rational numbers. Zbl 1432.11031
Platonov, Vladimir P.
3
2017
\(S\)-units in hyperelliptic fields and periodicity of continued fractions. Zbl 1392.11035
Platonov, V. P.; Petrunin, M. M.
13
2016
Continued rational fractions in hyperelliptic fields and the Mumford representation. Zbl 1403.11071
Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V.
13
2016
\(S\)-units and periodicity in quadratic function fields. Zbl 1357.11111
Platonov, V. P.; Petrunin, M. M.
13
2016
\(S\)-units and periodicity of continued fractions in hyperelliptic fields. Zbl 1337.11040
Platonov, V. P.; Fedorov, G. V.
14
2015
Fundamental \(S\)-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves. Zbl 1348.14083
Platonov, 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 1356.11038
Platonov, 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 1305.11096
Platonov, V. P.
32
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 1278.14045
Platonov, 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 1319.11041
Platonov, V. P.; Petrunin, M. M.
10
2012
Arithmetic of quadratic fields and torsion in Jacobians. Zbl 1217.11094
Platonov, V. P.
10
2010
A new local-global principle for quadratic function fields. Zbl 1244.11093
Benyash-Krivets, V. V.; Platonov, V. P.
5
2010
Arithmetic properties of quadratic function fields and torsion in Jacobians. Zbl 1320.11106
Platonov, V. P.
2
2010
New properties of arithmetic groups. Zbl 1214.20045
Platonov, V. P.
1
2010
Groups of \(S\)-units in hyperelliptic fields and continued fractions. Zbl 1231.11131
Benyash-Krivets, V. V.; Platonov, V. P.
22
2009
Continued fractions and \(S\)-units in hyperelliptic fields. Zbl 1225.11160
Benyash-Krivets, V. V.; Platonov, V. P.
3
2008
Continued fractions and \(S\)-units in function fields. Zbl 1221.11224
Benyash-Krivets, V. V.; Platonov, V. P.
1
2008
Groups of \(S\)-units in hyperelliptic fields. Zbl 1154.11039
Benyash-Krivets, V. V.; Platonov, V. P.
3
2007
\(S\)-units in hyperelliptic fields. Zbl 1176.11053
Benyash-Krivets, V. V.; Platonov, V. P.
1
2007
On the linearity of automorphism groups for free metabelian groups. Zbl 1155.20310
Platonov, V. P.
1
2006
New combinatorial properties of linear groups. Zbl 0983.20041
Platonov, Vladimir P.; Potapchik, Alexander
2
2001
Rigidity results for groups with radical cohomology of finite groups and arithmeticity problems. Zbl 1007.11029
Grunewald, Fritz; Platonov, Vladimir
6
1999
Solvable arithmetic groups and arithmeticity problems. Zbl 1039.20026
Grunewald, Fritz; Platonov, Vladimir
3
1999
Rigidity for groups with radical, cohomology of finite groups, and arithmeticity problems. Zbl 0941.20052
Platonov, V. P.
1
1999
The rationality problem for semisimple group varieties. Zbl 0904.20036
Chernousov, Vladimir I.; Platonov, Vladimir P.
7
1998
Non-arithmetic polycyclic groups. Zbl 0974.20035
Grunewald, Fritz; Platonov, Vladimir
2
1998
Rigidity and automorphism groups of solvable arithmetic groups. Zbl 0914.20043
Grunewald, Fritz; Platonov, Vladimir
2
1998
On finite extensions of arithmetic groups. Zbl 0913.20034
Grunewald, Fritz; Platonov, Vladimir
6
1997
Adelic profinite groups. Zbl 0884.20018
Platonov, V. P.; Sury, B.
2
1997
Subgroups of \(\text{GL}(n^ 2,\mathbf C)\) containing \(\text{PSU}(n)\). Zbl 0848.20033
Platonov, V. P.; Đoković, D. Ž.
6
1996
Low-dimensional representations of \(\text{Aut}(F_ 2)\). Zbl 0862.20006
Đoković, Dragomir Ž.; Platonov, Vladimir P.
5
1996
Linear preserver problems and algebraic groups. Zbl 0836.20065
Platonov, Vladimir P.; Đoković, Dragomir Ž.
13
1995
Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046
Platonov, Vladimir; Rapinchuk, Andrei
254
1994
Subgroups of algebraic groups over a local or global field containing a maximal torus. Zbl 0831.20062
Platonov, Vladimir P.
3
1994
Algebraic groups and linear preserver problems. Zbl 0811.20044
Đoković, Dragomir Ž.; Platonov, Vladimir P.
6
1993
Algebraic groups and number theory. Zbl 0806.11002
Platonov, V. P.; Rapinchuk, A. S.
101
1992
Abstract properties of \(S\)-arithmetic groups and the congruence problem. Zbl 0785.20025
Platonov, V. P.; Rapinchuk, A. S.
10
1992
Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027
Platonov, V. P.; Rapinchuk, A. S.
45
1991
Character rings of representations of finitely generated groups. Zbl 0766.20008
Platonov, V. P.; Benyash-Krivets, V. V.
5
1990
Grothendieck’s problem on profinite completions and representations of groups. Zbl 0722.20020
Platonov, V. P.; Tavgen’, O. I.
1
1990
Rings and varieties of representations of finitely generated groups. Zbl 0765.20011
Platonov, V. P.
5
1989
Finite-dimensional Henselian division algebras. Zbl 0669.16016
Platonov, V. P.; Yanchevskij, V. I.
3
1988
On the theory of Henselian division algebras. Zbl 0667.16018
Platonov, V. P.; Yanchevskij, V. I.
2
1988
The Hasse norm principle for algebraic number fields. Zbl 0624.12009
Drakokhrust, Yu. A.; Platonov, V. P.
6
1987
Character rings of \(n\)-dimensional representations of finitely generated groups. Zbl 0669.20004
Platonov, V. P.; Benyash-Krivets, V. V.
1
1987
On Grothendieck’s problem on profinite completions of groups. Zbl 0614.20016
Platonov, 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 0593.16012
Platonov, V. P.; Yanchevskij, V. I.
4
1985
The multiplicative structure of division rings over number fields and the Hasse norm principle. Zbl 0579.12010
Platonov, V. P.; Rapinchuk, A. S.
1
1985
On the Hasse principle for algebraic number fields. Zbl 0604.12011
Platonov, V. P.; Drakokhrust, Yu. A.
1
1985
The Hasse norm principle for primary extensions of algebraic number fields. Zbl 0604.12012
Platonov, V. P.; Drakokhrust, Yu. A.
1
1985
Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010
Platonov, 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 0579.16011
Platonov, V. P.; Yanchevskij, V. I.
2
1984
Dieudonné’s conjecture on the structure of unitary groups, and division rings over Henselian fields. Zbl 0595.16017
Platonov, V. P.; Yanchevskij, V. I.
1
1984
Algebraic groups. Zbl 0564.20023
Platonov, V. P.; Rapinchuk, A. S.
2
1983
Birational properties of spinor varieties. Zbl 0522.14004
Platonov, V. P.
1
1983
Arithmetic theory of algebraic groups. Zbl 0502.20025
Platonov, V. P.
10
1982
The arithmetic theory of algebraic groups. Zbl 0513.20028
Platonov, V. P.
3
1982
The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029
Platonov, V. P.; Rapinchuk, A. S.
3
1982
Birational properties of spinor varieties. Zbl 0496.14008
Platonov, V. P.
3
1981
Class numbers and groups of algebraic groups. II. Zbl 0464.20031
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1
1981
Algebraic groups and reduced K-theory. Zbl 0425.16018
Platonov, V. P.
6
1980
On the rationality of canonical spinor varieties. Zbl 0486.14013
Platonov, V. P.; Chernousov, V. I.
4
1980
Class numbers and groups of algebraic groups. Zbl 0448.20045
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1
1980
Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033
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.
2
1979
Correction. Zbl 0419.16013
Platonov, V. P.; Yanchevskij, V. I.
1
1979
On the problem of rationality of spinor varieties. Zbl 0435.20028
Platonov, V. P.
1
1979
On reduced K-theory for n-fold Hensel fields. Zbl 0436.13008
Platonov, V. P.
1
1979
The Tannaka-Artin problem and reduced K-theory. Zbl 0349.16008
Platonov, V. P.
12
1977
Birational properties of the reduced Whitehead group. Zbl 0791.20045
Platonov, V. P.
3
1977
Das Tannaka-Artinsche Problem und reduzierte K-Theorie. Zbl 0338.16005
Platonov, V. P.
12
1976
Die Unendlichkeit der reduzierten Whiteheadgruppe im Tannaka-Artin- Problem. Zbl 0352.16009
Platonov, V. P.
5
1976
Reduced K-theory and approximation in algebraic groups. Zbl 0417.16012
Platonov, V. P.
2
1976
The reduced Whitehead group for cyclic algebras. Zbl 0345.16023
Platonov, V. P.
2
1976
On the infiniteness of the reduced Whitehead group. Zbl 0362.16009
Platonov, V. P.
2
1976
Bemerkungen zu meiner Arbeit ”Das Tannaka-Artin Problem und reduzierte K- Theorie”. Zbl 0343.16014
Platonov, V. P.
1
1976
On the Tannaka-Artin problem. Zbl 0333.20032
Platonov, V. P.
10
1975
On Harder’s conjecture. Zbl 0333.20035
Platonov, V. P.; Yanchevskii, V. I.
4
1975
A problem of Tannaka-Artin and groups of projective conorms. Zbl 0338.16004
Platonov, V. P.
4
1975
On the Kneser-Tits conjecture for unitary groups. Zbl 0343.16016
Platonov, V. P.; Yanchevskii, V. I.
3
1975
The arithmetic theory of linear algebraic groups and number theory. Zbl 0305.20023
Platonov, V. P.
1
1975
Dieudonne’s conjecture and the nonsurjectivity on k-points of coverings of algebraic groups. Zbl 0348.20040
Platonov, V. P.
2
1974
Determination of algebraic groups by arithmetic subgroups. Zbl 0312.20024
Platonov, V. P.; Milovanov, M. V.
6
1973
The structure of unitary groups and the commutator group of a simple algebra over global fields. Zbl 0298.20035
Platonov, V. P.; Yanchevskii, V. I.
5
1973
Arithmetische Theorie der linearen algebraischen Gruppen und die Zahlentheorie. Zbl 0289.20024
Platonov, V. P.
1
1973
On the congruence problem for linear groups over arithmetic rings. Zbl 0791.20052
Platonov, V. P.; Sharomet, A. A.
1
1972
...and 27 more Documents
all top 5

Cited by 610 Authors

37 Platonov, Vladimir Petrovich
25 Rapinchuk, Andrei S.
16 Petrunin, Maksim Maksimovich
15 Fëdorov, Gleb Vladimirovich
15 Lubotzky, Alexander
13 Chernousov, Vladimir I.
13 Grunewald, Fritz J.
11 Nguyễn Quôc Thăng
10 Prasad, Gopal
8 Einsiedler, Manfred Leopold
7 Hazrat, Roozbeh
7 Kunyavskiĭ, Boris Èmmanuilovich
7 Margulis, Grigoriĭ Aleksandrovich
7 Parimala, Raman
7 Witte Morris, Dave
6 Belolipetsky, Mikhail V.
6 Gelander, Tsachik
6 Gordeev, Nikolai L.
6 Guralnick, Robert Michael
6 Kaletha, Tasho
6 Oh, Hee
6 Rapinchuk, Igor A.
6 Yanchevskii, Vyacheslav Ivanovich
6 Zhgoon, Vladimir S.
5 Avni, Nir
5 Borovoi, Mikhail V.
5 Cao, Yang
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 Wesolek, Phillip Richard
5 Zalesskii, Pavel
4 Aka, Menny
4 Arenas-Carmona, Luis
4 Bader, Uri
4 Benyash-Krivets, Valeriĭ Vatslavovich
4 Bitan, Rony A.
4 Bridson, Martin R.
4 Choiy, Kwangho
4 Đoković, Dragomir Ž.
4 Draper, Cristina
4 Gorodnik, Alexander
4 Martín González, Cándido
4 McReynolds, David Ben
4 Merkur’ev, Aleksandr Sergeevich
4 Raghunathan, Madabusi Santanam
4 Segal, Daniel
4 Shteĭnikov, Yuriĭ Nikolaevich
4 Stover, Matthew
4 Sury, Balasubramanian
4 Vavilov, Nikolaĭ Aleksandrovich
4 Venkataramana, Tyakal Nanjundiah
4 Wadsworth, Adrian R.
4 Wei, Dasheng
4 Wortman, Kevin A.
4 Yafaev, Andrei
4 Zalesski, Alexandre Efimovich
3 Bou-Rabee, Khalid
3 Bukhshtaber, Viktor Matveevich
3 Calderón Martín, Antonio Jesús
3 Chan, Wai Kiu
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 Klopsch, Benjamin
3 Koibaev, Vladimir Amurkhanovich
3 Larsen, Michael Jeffrey
3 Liebeck, Martin Walter
3 Lim, Seonhee
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 Potapchik, Alexander
3 Rehmann, Ulf
3 Rohlfs, Jürgen
3 Samuels, Beth
3 Sauer, Roman
3 Šemrl, Peter
3 Shapira, Uri
3 Sorensen, Claus Mazanti
3 Taïbi, Olivier
3 Thakur, Maneesh L.
3 Thorne, Jack A.
3 Tignol, Jean-Pierre
3 Tomanov, Georges Metodiev
3 Ullmo, Emmanuel
3 Venkatesh, Akshay
...and 510 more Authors
all top 5

Cited in 133 Serials

64 Journal of Algebra
29 Duke Mathematical Journal
28 Doklady Mathematics
25 Transactions of the American Mathematical Society
24 Journal of Number Theory
22 Mathematische Zeitschrift
21 Israel Journal of Mathematics
19 Inventiones Mathematicae
16 Journal of Mathematical Sciences (New York)
13 Advances in Mathematics
13 Geometriae Dedicata
13 Journal of Soviet Mathematics
13 Proceedings of the American Mathematical Society
12 Mathematische Annalen
11 Mathematical Notes
11 Journal of the American Mathematical Society
10 Compositio Mathematica
10 Linear Algebra and its Applications
10 Chebyshevskiĭ Sbornik
9 Communications in Algebra
9 Annales de l’Institut Fourier
9 Publications Mathématiques
9 Manuscripta Mathematica
9 Annals of Mathematics. Second Series
8 Siberian Mathematical Journal
8 Journal of the European Mathematical Society (JEMS)
7 Ukrainian Mathematical Journal
7 Proceedings of the Steklov Institute of Mathematics
7 Forum of Mathematics, Sigma
6 Journal für die Reine und Angewandte Mathematik
6 Geometric and Functional Analysis. GAFA
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 Geometry & Topology
4 Journal d’Analyse Mathématique
4 Michigan Mathematical Journal
4 \(K\)-Theory
4 Proceedings of the Indian Academy of Sciences. Mathematical Sciences
4 Representation Theory
4 Comptes Rendus. Mathématique. Académie des Sciences, Paris
4 Journal of the Institute of Mathematics of Jussieu
3 Russian Mathematical Surveys
3 Algebra and Logic
3 Archiv der Mathematik
3 Nagoya Mathematical Journal
3 Proceedings of the London Mathematical Society. Third Series
3 Forum Mathematicum
3 International Journal of Mathematics
3 Groups, Geometry, and Dynamics
3 Algebra & Number Theory
2 Communications in Mathematical Physics
2 Mathematical Proceedings of the Cambridge Philosophical Society
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 International Journal of Algebra and Computation
2 Journal de Théorie des Nombres de Bordeaux
2 St. Petersburg Mathematical Journal
2 Bulletin des Sciences Mathématiques
2 Transformation Groups
2 Trudy Instituta Matematiki
2 Algebraic & Geometric Topology
2 SIGMA. Symmetry, Integrability and Geometry: Methods and Applications
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 The Journal of Symbolic Logic
1 Kodai Mathematical Journal
1 Mathematika
1 Pacific Journal of Mathematics
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
1 Combinatorica
1 Annals of Pure and Applied Logic
1 Bulletin of the Iranian Mathematical Society
1 Revista Matemática Iberoamericana
...and 33 more Serials
all top 5

Cited in 41 Fields

314 Number theory (11-XX)
294 Group theory and generalizations (20-XX)
174 Topological groups, Lie groups (22-XX)
149 Algebraic geometry (14-XX)
63 Associative rings and algebras (16-XX)
35 Dynamical systems and ergodic theory (37-XX)
34 Manifolds and cell complexes (57-XX)
33 Field theory and polynomials (12-XX)
28 Nonassociative rings and algebras (17-XX)
24 Linear and multilinear algebra; matrix theory (15-XX)
22 Differential geometry (53-XX)
20 \(K\)-theory (19-XX)
13 Geometry (51-XX)
12 Category theory; homological algebra (18-XX)
12 Several complex variables and analytic spaces (32-XX)
11 Combinatorics (05-XX)
10 Global analysis, analysis on manifolds (58-XX)
8 Mathematical logic and foundations (03-XX)
7 Measure and integration (28-XX)
6 Operator theory (47-XX)
6 Algebraic topology (55-XX)
5 Abstract harmonic analysis (43-XX)
5 Functional analysis (46-XX)
4 History and biography (01-XX)
4 Functions of a complex variable (30-XX)
3 Commutative algebra (13-XX)
3 Convex and discrete geometry (52-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 Special functions (33-XX)
1 Ordinary differential equations (34-XX)
1 Partial differential equations (35-XX)
1 Approximations and expansions (41-XX)
1 Harmonic analysis on Euclidean spaces (42-XX)
1 Statistics (62-XX)
1 Biology and other natural sciences (92-XX)

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