Compute Distance To:
 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
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### 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
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### 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)

### 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 0841.20046
1994
Algebraic groups and number theory. Zbl 0806.11002
Platonov, V. P.; Rapinchuk, A. S.
1992
Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027
Platonov, V. P.; Rapinchuk, A. S.
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.
2014
Groups of $$S$$-units in hyperelliptic fields and continued fractions. Zbl 1231.11131
Benyash-Krivets, V. V.; Platonov, V. P.
2009
On the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1445.11135
Platonov, V. P.; Fedorov, G. V.
2018
The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups. Zbl 0217.36301
Platonov, V. P.
1971
$$S$$-units and periodicity of continued fractions in hyperelliptic fields. Zbl 1337.11040
Platonov, V. P.; Fedorov, G. V.
2015
Locally projectively nilpotent subgroups and nilelements in topological groups. Zbl 0222.22002
Platonov, V. P.
1966
Linear preserver problems and algebraic groups. Zbl 0836.20065
Platonov, Vladimir P.; Đoković, Dragomir Ž.
1995
Groups of $$S$$-units and the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1440.11127
Platonov, V. P.; Petrunin, M. M.
2018
Continued rational fractions in hyperelliptic fields and the Mumford representation. Zbl 1403.11071
Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V.
2016
On the periodicity of continued fractions in hyperelliptic fields. Zbl 1418.11109
Platonov, V. P.; Fedorov, G. V.
2017
$$S$$-units in hyperelliptic fields and periodicity of continued fractions. Zbl 1392.11035
Platonov, V. P.; Petrunin, M. M.
2016
$$S$$-units and periodicity in quadratic function fields. Zbl 1357.11111
Platonov, V. P.; Petrunin, M. M.
2016
Abstract properties of $$S$$-arithmetic groups and the congruence problem. Zbl 0785.20025
Platonov, V. P.; Rapinchuk, A. S.
1992
Das Tannaka-Artinsche Problem und reduzierte K-Theorie. Zbl 0338.16005
Platonov, V. P.
1976
The Tannaka-Artin problem and reduced K-theory. Zbl 0349.16008
Platonov, V. P.
1977
Arithmetic theory of algebraic groups. Zbl 0502.20025
Platonov, V. P.
1982
On the Tannaka-Artin problem. Zbl 0333.20032
Platonov, V. P.
1975
On the periodicity of continued fractions in elliptic fields. Zbl 1392.11048
Platonov, V. P.; Fedorov, G. V.
2017
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.
2012
Arithmetic of quadratic fields and torsion in Jacobians. Zbl 1217.11094
Platonov, V. P.
2010
On the finiteness of the number of elliptic fields with given degrees of $$S$$-units and periodic expansion of $$\sqrt f$$. Zbl 1477.11187
Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N.
2019
The Hasse norm principle for algebraic number fields. Zbl 0624.12009
Drakokhrust, Yu. A.; Platonov, V. P.
1987
The rationality problem for semisimple group varieties. Zbl 0904.20036
1998
Engel elements and the radical in PI-algebras and topological groups. Zbl 0136.29503
Platonov, V. P.
1965
On the group of rational points of three-dimensional groups. Zbl 0431.12012
Platonov, V. P.; Rapinchuk, A. S.
1979
Linear algebraic groups. (Linejnye algebraicheskie gruppy.) Übersetzung aus dem Englischen von A. E. Zalesskii. Herausgegeben von V. P. Platonov. Zbl 0235.22017
Borel, Armand
1972
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.
2018
Theory of algebraic linear groups and periodic groups. Zbl 0177.04802
Platonov, V. P.
1968
Fundamental $$S$$-units in hyperelliptic fields and the torsion problem in Jacobians of hyperelliptic curves. Zbl 1348.14083
Platonov, V. P.; Petrunin, M. M.
2015
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.
2018
On Grothendieck’s problem on profinite completions of groups. Zbl 0614.20016
Platonov, V. P.; Tavgen’, O. I.
1986
Algebraic groups and reduced K-theory. Zbl 0425.16018
Platonov, V. P.
1980
Subgroups of $$\text{GL}(n^ 2,\mathbf C)$$ containing $$\text{PSU}(n)$$. Zbl 0848.20033
Platonov, V. P.; Đoković, D. Ž.
1996
Determination of algebraic groups by arithmetic subgroups. Zbl 0312.20024
Platonov, V. P.; Milovanov, M. V.
1973
Rigidity results for groups with radical cohomology of finite groups and arithmeticity problems. Zbl 1007.11029
1999
On finite extensions of arithmetic groups. Zbl 0913.20034
1997
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.
1969
Algebraic groups and linear preserver problems. Zbl 0811.20044
Đoković, Dragomir Ž.; Platonov, Vladimir P.
1993
A certain problem for finitely generated groups. Zbl 0228.20018
Platonov, V. P.
1968
Rings and varieties of representations of finitely generated groups. Zbl 0765.20011
Platonov, V. P.
1989
Character rings of representations of finitely generated groups. Zbl 0766.20008
Platonov, V. P.; Benyash-Krivets, V. V.
1990
On the problem of classification of periodic continued fractions in hyperelliptic fields. Zbl 1451.11127
Platonov, V. P.; Fedorov, G. V.
2020
The Frattini subgroup of linear groups and finite approximability. Zbl 0242.20038
Platonov, V. P.
1966
Lokal projective nilpotent radicals in topological groups. Zbl 0242.22006
Platonov, V. P.
1965
Low-dimensional representations of $$\text{Aut}(F_ 2)$$. Zbl 0862.20006
Đoković, Dragomir Ž.; Platonov, Vladimir P.
1996
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.
1973
Die Unendlichkeit der reduzierten Whiteheadgruppe im Tannaka-Artin- Problem. Zbl 0352.16009
Platonov, V. P.
1976
A new local-global principle for quadratic function fields. Zbl 1244.11093
Benyash-Krivets, V. V.; Platonov, V. P.
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 1278.14045
Platonov, V. P.; Zhgun, V. S.; Petrunin, M. M.
2013
Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010
Platonov, V. P.; Rapinchuk, A. S.
1984
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.
1985
On the rationality of canonical spinor varieties. Zbl 0486.14013
Platonov, V. P.; Chernousov, V. I.
1980
On Harder’s conjecture. Zbl 0333.20035
Platonov, V. P.; Yanchevskii, V. I.
1975
A problem of Tannaka-Artin and groups of projective conorms. Zbl 0338.16004
Platonov, V. P.
1975
Solvable arithmetic groups and arithmeticity problems. Zbl 1039.20026
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 1427.14062
Platonov, V. P.; Fedorov, G. V.
2018
The arithmetic theory of algebraic groups. Zbl 0513.20028
Platonov, V. P.
1982
The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029
Platonov, V. P.; Rapinchuk, A. S.
1982
Finite-dimensional Henselian division algebras. Zbl 0669.16016
Platonov, V. P.; Yanchevskij, V. I.
1988
On the maximality problem for arithmetic groups. Zbl 0252.20050
Platonov, V. P.
1971
On the Kneser-Tits conjecture for unitary groups. Zbl 0343.16016
Platonov, V. P.; Yanchevskii, V. I.
1975
Continued fractions and $$S$$-units in hyperelliptic fields. Zbl 1225.11160
Benyash-Krivets, V. V.; Platonov, V. P.
2008
Groups of $$S$$-units in hyperelliptic fields. Zbl 1154.11039
Benyash-Krivets, V. V.; Platonov, V. P.
2007
Non-arithmetic polycyclic groups. Zbl 0974.20035
1998
Structure of topological locally projectively nilpotent groups, and of groups with a normalizer condition. Zbl 0164.34203
Platonov, V. P.
1968
Certain classes of topological groups. Zbl 0166.02701
Platonov, V. P.
1966
The structure of periodic linear groups and algebraic groups. Zbl 0171.28802
Platonov, V. P.
1966
Some remarks on linear groups. Zbl 0215.39701
Platonov, V. P.
1968
On new properties of Hankel matrices over the field of rational numbers. Zbl 1432.11031
2017
Birational properties of the reduced Whitehead group. Zbl 0791.20045
Platonov, V. P.
1977
On Auerbach’s problem. Zbl 0225.20025
Platonov, V. P.; Zalesskij, A. E.
1966
Birational properties of spinor varieties. Zbl 0496.14008
Platonov, V. P.
1981
New combinatorial properties of linear groups. Zbl 0983.20041
2001
Subgroups of algebraic groups over a local or global field containing a maximal torus. Zbl 0831.20062
1994
On new arithmetic properties of determinants of Hankel matrices. Zbl 1400.15012
Platonov, V. P.; Petrunin, M. M.
2018
Algebraic groups. Zbl 0564.20023
Platonov, V. P.; Rapinchuk, A. S.
1983
On the theory of Henselian division algebras. Zbl 0667.16018
Platonov, V. P.; Yanchevskij, V. I.
1988
Reduced K-theory and approximation in algebraic groups. Zbl 0417.16012
Platonov, V. P.
1976
Class number of algebraic groups. Zbl 0425.20038
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1979
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.
1984
Addendum to the paper ”The problem of strong approximation and the Kneser-Tits conjecture for algebraic groups”. Zbl 0236.20034
Platonov, V. P.
1971
On the genus problem in arithmetic groups. Zbl 0256.20059
Platonov, V. P.
1971
Algebraische d-Gruppen. Zbl 0274.20059
Platonov, V. P.
1963
The reduced Whitehead group for cyclic algebras. Zbl 0345.16023
Platonov, V. P.
1976
Dieudonne’s conjecture and the nonsurjectivity on k-points of coverings of algebraic groups. Zbl 0348.20040
Platonov, V. P.
1974
On the infiniteness of the reduced Whitehead group. Zbl 0362.16009
Platonov, V. P.
1976
Grothendieck’s problem on profinite completions and representations of groups. Zbl 0722.20020
Platonov, V. P.; Tavgen’, O. I.
1990
Rigidity and automorphism groups of solvable arithmetic groups. Zbl 0914.20043
1998
Automorphisms of algebraic groups. Zbl 0158.27802
Platonov, V. P.
1966
Proof of the finiteness hypothesis for the solvable subgroups of algebraic groups. Zbl 0196.05203
Platonov, V. P.
1970
Splittable linear groups. Zbl 0227.20016
Platonov, V. P.
1963
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.
2015
Arithmetic properties of quadratic function fields and torsion in Jacobians. Zbl 1320.11106
Platonov, V. P.
2010
Platonov, V. P.; Sury, B.
1997
The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. Zbl 1439.11286
2019
Birational properties of spinor varieties. Zbl 0522.14004
Platonov, V. P.
1983
Dieudonné’s conjecture on the structure of unitary groups, and division rings over Henselian fields. Zbl 0595.16017
Platonov, V. P.; Yanchevskij, V. I.
1984
On the classification problem for polynomials $$f$$ with a periodic continued fraction expansion of $$\sqrt{f}$$ in hyperelliptic fields. Zbl 1483.11123
Platonov, V. P.; Fedorov, G. V.
2021
On the problem of classification of periodic continued fractions in hyperelliptic fields. Zbl 1451.11127
Platonov, V. P.; Fedorov, G. V.
2020
On the finiteness of the number of expansions into a continued fraction of $$\sqrt f$$ for cubic polynomials over algebraic number fields. Zbl 1479.11202
Platonov, V. P.; Petrunin, M. M.
2020
On the finiteness of the number of elliptic fields with given degrees of $$S$$-units and periodic expansion of $$\sqrt f$$. Zbl 1477.11187
Platonov, V. P.; Petrunin, M. M.; Shteinikov, Yu. N.
2019
The criterion of periodicity of continued fractions of key elements in hyperelliptic fields. Zbl 1439.11286
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.
2019
On infinite-dimensional integer Hankel matrices. Zbl 1419.15027
Platonov, V. P.; Petrunin, M. M.
2019
On the problem of periodicity of continued fractions in hyperelliptic fields. Zbl 1445.11135
Platonov, V. P.; Fedorov, G. V.
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.
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.
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.
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.
2018
On new arithmetic properties of determinants of Hankel matrices. Zbl 1400.15012
Platonov, V. P.; Petrunin, M. M.
2018
On the periodicity of continued fractions in hyperelliptic fields. Zbl 1418.11109
Platonov, V. P.; Fedorov, G. V.
2017
On the periodicity of continued fractions in elliptic fields. Zbl 1392.11048
Platonov, V. P.; Fedorov, G. V.
2017
On new properties of Hankel matrices over the field of rational numbers. Zbl 1432.11031
2017
Continued rational fractions in hyperelliptic fields and the Mumford representation. Zbl 1403.11071
Platonov, V. P.; Zhgoon, V. S.; Fedorov, G. V.
2016
$$S$$-units in hyperelliptic fields and periodicity of continued fractions. Zbl 1392.11035
Platonov, V. P.; Petrunin, M. M.
2016
$$S$$-units and periodicity in quadratic function fields. Zbl 1357.11111
Platonov, V. P.; Petrunin, M. M.
2016
$$S$$-units and periodicity of continued fractions in hyperelliptic fields. Zbl 1337.11040
Platonov, V. P.; Fedorov, G. V.
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.
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.
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.
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.
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.
2012
Arithmetic of quadratic fields and torsion in Jacobians. Zbl 1217.11094
Platonov, V. P.
2010
A new local-global principle for quadratic function fields. Zbl 1244.11093
Benyash-Krivets, V. V.; Platonov, V. P.
2010
Arithmetic properties of quadratic function fields and torsion in Jacobians. Zbl 1320.11106
Platonov, V. P.
2010
New properties of arithmetic groups. Zbl 1214.20045
Platonov, V. P.
2010
Groups of $$S$$-units in hyperelliptic fields and continued fractions. Zbl 1231.11131
Benyash-Krivets, V. V.; Platonov, V. P.
2009
Continued fractions and $$S$$-units in hyperelliptic fields. Zbl 1225.11160
Benyash-Krivets, V. V.; Platonov, V. P.
2008
Continued fractions and $$S$$-units in function fields. Zbl 1221.11224
Benyash-Krivets, V. V.; Platonov, V. P.
2008
Groups of $$S$$-units in hyperelliptic fields. Zbl 1154.11039
Benyash-Krivets, V. V.; Platonov, V. P.
2007
$$S$$-units in hyperelliptic fields. Zbl 1176.11053
Benyash-Krivets, V. V.; Platonov, V. P.
2007
On the linearity of automorphism groups for free metabelian groups. Zbl 1155.20310
Platonov, V. P.
2006
New combinatorial properties of linear groups. Zbl 0983.20041
2001
Rigidity results for groups with radical cohomology of finite groups and arithmeticity problems. Zbl 1007.11029
1999
Solvable arithmetic groups and arithmeticity problems. Zbl 1039.20026
1999
Rigidity for groups with radical, cohomology of finite groups, and arithmeticity problems. Zbl 0941.20052
Platonov, V. P.
1999
The rationality problem for semisimple group varieties. Zbl 0904.20036
1998
Non-arithmetic polycyclic groups. Zbl 0974.20035
1998
Rigidity and automorphism groups of solvable arithmetic groups. Zbl 0914.20043
1998
On finite extensions of arithmetic groups. Zbl 0913.20034
1997
Platonov, V. P.; Sury, B.
1997
Subgroups of $$\text{GL}(n^ 2,\mathbf C)$$ containing $$\text{PSU}(n)$$. Zbl 0848.20033
Platonov, V. P.; Đoković, D. Ž.
1996
Low-dimensional representations of $$\text{Aut}(F_ 2)$$. Zbl 0862.20006
Đoković, Dragomir Ž.; Platonov, Vladimir P.
1996
Linear preserver problems and algebraic groups. Zbl 0836.20065
Platonov, Vladimir P.; Đoković, Dragomir Ž.
1995
Algebraic groups and number theory. Transl. from the Russian by Rachel Rowen. Zbl 0841.20046
1994
Subgroups of algebraic groups over a local or global field containing a maximal torus. Zbl 0831.20062
1994
Algebraic groups and linear preserver problems. Zbl 0811.20044
Đoković, Dragomir Ž.; Platonov, Vladimir P.
1993
Algebraic groups and number theory. Zbl 0806.11002
Platonov, V. P.; Rapinchuk, A. S.
1992
Abstract properties of $$S$$-arithmetic groups and the congruence problem. Zbl 0785.20025
Platonov, V. P.; Rapinchuk, A. S.
1992
Algebraic groups and number theory. (Алгебраические группы и теория чисел.) Zbl 0732.20027
Platonov, V. P.; Rapinchuk, A. S.
1991
Character rings of representations of finitely generated groups. Zbl 0766.20008
Platonov, V. P.; Benyash-Krivets, V. V.
1990
Grothendieck’s problem on profinite completions and representations of groups. Zbl 0722.20020
Platonov, V. P.; Tavgen&rsquo;, O. I.
1990
Rings and varieties of representations of finitely generated groups. Zbl 0765.20011
Platonov, V. P.
1989
Finite-dimensional Henselian division algebras. Zbl 0669.16016
Platonov, V. P.; Yanchevskij, V. I.
1988
On the theory of Henselian division algebras. Zbl 0667.16018
Platonov, V. P.; Yanchevskij, V. I.
1988
The Hasse norm principle for algebraic number fields. Zbl 0624.12009
Drakokhrust, Yu. A.; Platonov, V. P.
1987
Character rings of $$n$$-dimensional representations of finitely generated groups. Zbl 0669.20004
Platonov, V. P.; Benyash-Krivets, V. V.
1987
On Grothendieck’s problem on profinite completions of groups. Zbl 0614.20016
Platonov, V. P.; Tavgen&rsquo;, O. I.
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.
1985
On the Hasse principle for algebraic number fields. Zbl 0604.12011
Platonov, V. P.; Drakokhrust, Yu. A.
1985
The Hasse norm principle for primary extensions of algebraic number fields. Zbl 0604.12012
Platonov, V. P.; Drakokhrust, Yu. A.
1985
The multiplicative structure of division rings over number fields and the Hasse norm principle. Zbl 0579.12010
Platonov, V. P.; Rapinchuk, A. S.
1985
Multiplicative structure of skew fields over number fields and Hasse norm principle. Zbl 0559.12010
Platonov, V. P.; Rapinchuk, A. S.
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.
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.
1984
Algebraic groups. Zbl 0564.20023
Platonov, V. P.; Rapinchuk, A. S.
1983
Birational properties of spinor varieties. Zbl 0522.14004
Platonov, V. P.
1983
Arithmetic theory of algebraic groups. Zbl 0502.20025
Platonov, V. P.
1982
The arithmetic theory of algebraic groups. Zbl 0513.20028
Platonov, V. P.
1982
The multiplicative structure of division rings over number fields, and the Hasse principle. Zbl 0516.20029
Platonov, V. P.; Rapinchuk, A. S.
1982
Birational properties of spinor varieties. Zbl 0496.14008
Platonov, V. P.
1981
Class numbers and groups of algebraic groups. II. Zbl 0464.20031
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1981
Algebraic groups and reduced K-theory. Zbl 0425.16018
Platonov, V. P.
1980
On the rationality of canonical spinor varieties. Zbl 0486.14013
Platonov, V. P.; Chernousov, V. I.
1980
Class numbers and groups of algebraic groups. Zbl 0448.20045
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1980
Klassenzahlen und Klassengruppen algebraischer Gruppen. II. Zbl 0453.20033
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1980
On the group of rational points of three-dimensional groups. Zbl 0431.12012
Platonov, V. P.; Rapinchuk, A. S.
1979
Class number of algebraic groups. Zbl 0425.20038
Platonov, V. P.; Bondarenko, A. A.; Rapinchuk, A. S.
1979
Correction. Zbl 0419.16013
Platonov, V. P.; Yanchevskij, V. I.
1979
On the problem of rationality of spinor varieties. Zbl 0435.20028
Platonov, V. P.
1979
On reduced K-theory for n-fold Hensel fields. Zbl 0436.13008
Platonov, V. P.
1979
The Tannaka-Artin problem and reduced K-theory. Zbl 0349.16008
Platonov, V. P.
1977
Birational properties of the reduced Whitehead group. Zbl 0791.20045
Platonov, V. P.
1977
Das Tannaka-Artinsche Problem und reduzierte K-Theorie. Zbl 0338.16005
Platonov, V. P.
1976
Die Unendlichkeit der reduzierten Whiteheadgruppe im Tannaka-Artin- Problem. Zbl 0352.16009
Platonov, V. P.
1976
Reduced K-theory and approximation in algebraic groups. Zbl 0417.16012
Platonov, V. P.
1976
The reduced Whitehead group for cyclic algebras. Zbl 0345.16023
Platonov, V. P.
1976
On the infiniteness of the reduced Whitehead group. Zbl 0362.16009
Platonov, V. P.
1976
Bemerkungen zu meiner Arbeit ”Das Tannaka-Artin Problem und reduzierte K- Theorie”. Zbl 0343.16014
Platonov, V. P.
1976
On the Tannaka-Artin problem. Zbl 0333.20032
Platonov, V. P.
1975
On Harder’s conjecture. Zbl 0333.20035
Platonov, V. P.; Yanchevskii, V. I.
1975
A problem of Tannaka-Artin and groups of projective conorms. Zbl 0338.16004
Platonov, V. P.
1975
On the Kneser-Tits conjecture for unitary groups. Zbl 0343.16016
Platonov, V. P.; Yanchevskii, V. I.
1975
The arithmetic theory of linear algebraic groups and number theory. Zbl 0305.20023
Platonov, V. P.
1975
Dieudonne’s conjecture and the nonsurjectivity on k-points of coverings of algebraic groups. Zbl 0348.20040
Platonov, V. P.
1974
Determination of algebraic groups by arithmetic subgroups. Zbl 0312.20024
Platonov, V. P.; Milovanov, M. V.
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.
1973
...and 31 more Documents
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### 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
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### 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)

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