Edit Profile (opens in new tab) Vavilov, Nikolaĭ Aleksandrovich Co-Author Distance Author ID: vavilov.nikolai-a Published as: Vavilov, N. A.; Vavilov, Nikolai; Vavilov, N.; Vavilov, Nikolai A.; Vavilov, Nikolaĭ Aleksandrovich; Vavilov, Nikolaĭ A. more...less External Links: MGP · Math-Net.Ru Documents Indexed: 193 Publications since 1976 26 Contributions as Editor Biographic References: 2 Publications Co-Authors: 73 Co-Authors with 131 Joint Publications 1,471 Co-Co-Authors all top 5 Co-Authors 84 single-authored 29 Generalov, Aleksandr Ivanovich 29 Lur’e, Boris Beniaminovich 16 Borevich, Zenon Ivanovich 14 Zhang, Zuhong 13 Stepanov, Alexeĭ Vladimirovich 12 Hazrat, Roozbeh 7 Plotkin, Eugene 6 Luzgarev, A. Yu. 5 Panin, Ivan A. 4 Bak, Anthony 4 Dybkova, E. V. 4 Semenov, Alexey A. 4 Sinchuk, Sergeĭ Sergeevich 3 Gordeev, Nikolai L. 3 Kazakevich, V. G. 2 Anan’evskii, A. S. 2 Bondarko, Mikhail Vladimirovich 2 Di Martino, Lino 2 Gavrilovich, Mikhaĭl R. 2 Khamdan, I. 2 Kolotilina, Lily Yu. 2 Leonov, Gennadiĭ Alekseevich 2 Merkur’ev, Aleksandr Sergeevich 2 Narkiewicz, Władysław 2 Nesterov, Vladimir Viktorovich 2 Nikolenko, Sergey I. 2 Smolensky, A. V. 2 Stavrova, Anastasia K. 2 Sury, Balasubramanian 2 Suslin, Andreĭ Aleksandrovich 2 Vostokov, Sergeĭ Vladimirovich 2 Vsemirnov, Maxim 2 Yakovlev, Anatoliĭ Vladimirovich 2 Zhukov, Igor’ Borisovich 1 Aleksandrov, A. V. 1 Bakulin, S. V. 1 Batalkin, K. O. 1 Benois, D. G. 1 De Concini, Corrado 1 Fesenko, Ivan Borisovich 1 Harebov, Alan 1 Ishkanov, V. V. 1 Khalin, V. G. 1 Kharchev, N. P. 1 Kondrat’ev, Anatoliĭ Semenovich 1 Kovach, E. I. 1 Kunyavskiĭ, Boris Èmmanuilovich 1 Kusraev, Anatoly Georgievich 1 Makhnëv, Aleksandr Alekseevich 1 Matiyasevich, Yuriĭ Vladimirovich 1 Mazurov, Viktor Danilovich 1 Migrin, V. V. 1 Mitrofanov, M. Yu. 1 Mysovskikh, V. I. 1 Nuzhin, Yakov Nifant’evich 1 Pachev, Urusbi Mukhamedovich 1 Panov, Aleksandr Nikolaevich 1 Parshin, Alekseĭ Nikolaevich 1 Perelman, E. Ya. 1 Pevzner, Igor’ M. 1 Platonov, Vladimir Petrovich 1 Plotkin, Boris 1 Popov, Vladimir Leonidovich 1 Romanovskii, N. S. 1 Semenov, Andrei V. 1 Shchegolev, A. V. 1 Skopin, A. I. 1 Smirnov, Aleksandr Leonidovich 1 Teterin, Yu. G. 1 van Oystaeyen, Freddy 1 Vinberg, Èrnest Borisovich 1 Yurkov, A. V. 1 Zhurtov, Archil Khazeshevich all top 5 Serials 50 Journal of Mathematical Sciences (New York) 21 Journal of Soviet Mathematics 18 Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta Imeni V. A. Steklova 16 St. Petersburg Mathematical Journal 15 Zapiski Nauchnykh Seminarov POMI 12 Vestnik Leningrad University. Mathematics 7 Vestnik St. Petersburg University. Mathematics 5 Soviet Mathematics. Doklady 4 Vestnik Leningradskogo Universiteta. Matematika, Mekhanika, Astronomiya 4 Soviet Mathematics 3 Communications in Algebra 3 Izvestiya Vysshikh Uchebnykh Zavedeniĭ, Matematika 3 Russian Mathematical Surveys 3 Journal of Algebra 3 Doklady Mathematics 3 Proceedings of the Steklov Institute of Mathematics 3 Translations. Series 2. American Mathematical Society 2 Israel Journal of Mathematics 2 Mathematical Proceedings of the Cambridge Philosophical Society 2 Journal of Pure and Applied Algebra 2 Proceedings of the Edinburgh Mathematical Society. Series II 2 Siberian Mathematical Journal 2 \(K\)-Theory 2 International Journal of Algebra and Computation 2 Russian Academy of Sciences. Doklady. Mathematics 2 Vladikavkazskiĭ Matematicheskiĭ Zhurnal 2 Trudy Matematicheskogo Instituta Imeni V. A. Steklova 2 Journal of \(K\)-Theory 1 Uspekhi Matematicheskikh Nauk [N. S.] 1 Colloquium Mathematicum 1 Compositio Mathematica 1 Rendiconti del Seminario Matematico della Università di Padova 1 Sibirskiĭ Matematicheskiĭ Zhurnal 1 Note di Matematica 1 Acta Applicandae Mathematicae 1 Linear Algebra and its Applications 1 Bulletin de l’Académie Polonaise des Sciences. Série des Sciences Mathématiques 1 Algebra Colloquium 1 Trudy Sankt-Peterburgskogo Matematicheskogo Obshchestva 1 Transformation Groups 1 Voprosy Algebry 1 Trudy Instituta Matematiki 1 Vestnik Samarskogo Gosudarstvennogo Universitetea. Estestvennonauchnaya Seriya 1 Chebyshevskiĭ Sbornik 1 Lecture Notes in Pure and Applied Mathematics 1 International Journal of Group Theory 1 European Journal of Mathematics 1 Philosophical Transactions of the Royal Society of London. A. Mathematical, Physical and Engineering Sciences all top 5 Fields 206 Group theory and generalizations (20-XX) 30 Associative rings and algebras (16-XX) 28 General and overarching topics; collections (00-XX) 16 \(K\)-theory (19-XX) 13 Nonassociative rings and algebras (17-XX) 12 History and biography (01-XX) 9 Algebraic geometry (14-XX) 6 Number theory (11-XX) 6 Linear and multilinear algebra; matrix theory (15-XX) 4 Commutative algebra (13-XX) 1 Mathematical logic and foundations (03-XX) 1 Category theory; homological algebra (18-XX) 1 Computer science (68-XX) 1 Mathematics education (97-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 159 Publications have been cited 1,615 times in 342 Documents Cited by ▼ Year ▼ Decomposition of transvections: A theme with variations. Zbl 0944.20031Stepanov, Alexei; Vavilov, Nikolai 71 2000 Chevalley groups over commutative rings. I: Elementary calculations. Zbl 0861.20044Vavilov, Nikolai; Plotkin, Eugene 68 1996 Structure of hyperbolic unitary groups. I: Elementary subgroups. Zbl 0963.20024Bak, Anthony; Vavilov, Nikolai 67 2000 \(K_{1}\) of Chevalley groups are nilpotent. Zbl 1012.19001Hazrat, Roozbeh; Vavilov, Nikolai 62 2003 Structure of Chevalley groups over commutative rings. Zbl 0799.20042Vavilov, Nikolai A. 58 1991 A third look at weight diagrams. Zbl 1016.20029Vavilov, Nikolai 45 2000 Bak’s work on the \(K\)-theory of rings. Zbl 1183.19001Hazrat, Roozbeh; Vavilov, Nikolai 44 2009 Visual basic representations: An atlas. Zbl 0957.17006Plotkin, Eugene; Semenov, Andrei; Vavilov, Nikolai 44 1998 Normality for elementary subgroup functors. Zbl 0857.20028Bak, Anthony; Vavilov, Nikolai 36 1995 Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian. Zbl 1167.19002Bak, A.; Hazrat, R.; Vavilov, N. 33 2009 Structure of Chevalley groups: the proof from The Book. Zbl 1162.20032Vavilov, N. A.; Gavrilovich, M. R.; Nikolenko, S. I. 27 2006 Overgroups of semisimple groups. Zbl 1322.20040Vavilov, N. A.; Stepanov, A. V. 27 2008 Intermediate subgroups in Chevalley groups. Zbl 0879.20020Vavilov, Nikolai 26 1995 Commutator width in Chevalley groups. Zbl 1294.20059Hazrat, Roozbeh; Stepanov, Alexei; Vavilov, Nikolai; Zhang, Zuhong 26 2013 An \(A_3\)-proof of structure theorems for Chevalley groups of types \(E_6\) and \(E_7\). Zbl 1172.20034Vavilov, Nikolai 25 2007 Standard commutator formula. Zbl 1147.20042Vavilov, N. A.; Stepanov, A. V. 24 2008 Location of subgroups in the general linear group over a commutative ring. Zbl 0653.20048Borevich, Z. I.; Vavilov, N. A. 24 1985 The yoga of commutators. Zbl 1318.20049Hazrat, R.; Stepanov, A. V.; Vavilov, N. A.; Zhang, Z. 24 2011 Computations in Chevalley groups over commutative rings. Zbl 0795.20028Vavilov, N. A.; Plotkin, E. B.; Stepanov, A. V. 23 1989 Do it yourself: the structure constants for Lie algebras of types \(E_l\). Zbl 1062.17004Vavilov, N. A. 22 2001 Chevalley group of type \(E_6\) in the 27-dimensional representation. Zbl 1124.20032Vavilov, N. A.; Luzgarev, A. Yu.; Pevzner, I. M. 22 2006 On Grothendieck-Serre’s conjecture concerning principal \(G\)-bundles over reductive group schemes: I. Zbl 1317.14102Panin, I.; Stavrova, A.; Vavilov, N. 22 2015 On the length of commutators in Chevalley groups. Zbl 1262.20054Stepanov, Alexei; Vavilov, Nikolai 20 2011 \((2,3)\)-generation of \(SL(n,q)\). I: Cases \(n=5,6,7\). Zbl 0805.20038Di Martino, Lino; Vavilov, Nikolai 20 1994 Relative unitary commutator calculus, and applications. Zbl 1245.20064Hazrat, Roozbeh; Vavilov, Nikolai; Zhang, Zuhong 18 2011 An \(A_2\)-proof of structure theorems for Chevalley groups of types \(E_6\) and \(E_7\). Zbl 1105.20039Vavilov, N. A.; Gavrilovich, M. R. 18 2005 Subgroups of the general linear group over a semilocal ring which contain the group of diagonal matrices. Zbl 0444.20039Borevich, Z. I.; Vavilov, N. A. 17 1978 Relative commutator calculus in Chevalley groups. Zbl 1292.20053Hazrat, Roozbeh; Vavilov, Nikolai; Zhang, Zuhong 17 2013 Relative subgroups in Chevalley groups. Zbl 1204.20066Hazrat, R.; Petrov, V.; Vavilov, N. 16 2010 Standard commutator formula, revisited. Zbl 1254.20038Vavilov, N. A.; Stepanov, A. V. 16 2010 \((2,3)\)-generation of \(\text{SL}(n,q)\). II: Cases \(n\geq 8\). Zbl 0847.20043Di Martino, Lino; Vavilov, Nikolai 16 1996 On the overgroups of \(\text{EO}(2l,R)\). Zbl 1069.20040Vavilov, N. A.; Petrov, V. A. 15 2000 On the parabolic subgroups of Chevalley groups over a semilocal ring. Zbl 0448.20046Vavilov, N. A. 14 1978 On subgroups of splittable classical groups. Zbl 0723.20028Vavilov, N. A. 13 1990 Overgroups of elementary symplectic groups. Zbl 1075.20017Vavilov, N. A.; Petrov, V. A. 12 2004 Subgroups of split orthogonal groups over a ring. Zbl 0694.20032Vavilov, N. A. 12 1988 A note on the subnormal structure of general linear groups. Zbl 0701.20025Vavilov, N. A. 12 1990 \(A_2\)-proof of structure theorems for Chevalley groups of type \(F_4\). Zbl 1206.20055Vavilov, N. A.; Nikolenko, S. I. 11 2009 Subgroups of split orthogonal groups over a commutative ring. Zbl 1080.20046Vavilov, N. A. 11 2001 Generation of relative commutator subgroups in Chevalley groups. Zbl 1348.20055Hazrat, R.; Vavilov, N.; Zhang, Z. 11 2016 Subgroups of the general symplectic group containing the group of diagonal matrices. Zbl 0468.20041Vavilov, N. A.; Dybkova, E. V. 11 1980 Normalizer of the Chevalley group of type \(E_6\). Zbl 1206.20054Vavilov, N. A.; Luzgarev, A. Yu. 10 2008 On the lattice of subgroups of Chevalley groups containing a split maximal torus. Zbl 0857.20023Harebov, Alan; Vavilov, Nikolai 10 1996 Parabolic subgroups of Chevalley groups over a semilocal ring. Zbl 0612.20028Vavilov, N. A. 10 1987 The yoga of commutators: further applications. Zbl 1316.20055Hazrat, R.; Stepanov, A. V.; Vavilov, N. A.; Zhang, Z. 10 2014 The commutators of classical groups. Zbl 1393.20023Hazrat, R.; Vavilov, Nikolai; Zhang, Z. 9 2017 Multiple commutator formulas for unitary groups. Zbl 1403.20049Hazrat, R.; Vavilov, Nikolai; Zhang, Z. 9 2017 More variations on the decomposition of transvections. Zbl 1215.20048Vavilov, N. A.; Kazakevich, V. G. 9 2010 The structure of split classical groups over a commutative ring. Zbl 0688.20027Vavilov, N. A. 9 1988 Can one see the signs of structure constants? Zbl 1203.20041Vavilov, N. A. 9 2008 Overgroups of subsystem subgroups in exceptional groups: levels. Zbl 1301.20043Vavilov, N. A.; Shchegolev, A. V. 9 2013 Calculations in exceptional groups over rings. Zbl 1288.20063Luzgarev, A.; Stepanov, A.; Vavilov, N. 9 2010 Chevalley groups of type \(E_7\) in the 56-dimensional representation. Zbl 1306.20050Vavilov, N. A.; Luzgarev, A. Yu. 9 2012 On subgroups of split classical groups. Zbl 0741.20034Vavilov, N. A. 8 1990 Unitriangular factorizations of Chevalley groups. Zbl 1261.20051Vavilov, N. A.; Smolensky, A. V.; Sury, B. 8 2012 Overgroups of \(\text{EO}(n,R)\). Zbl 1159.20024Vavilov, N. A.; Petrov, V. A. 8 2008 Linear groups over general rings. I: Generalities. Zbl 1278.20066Vavilov, N. A.; Stepanov, A. V. 8 2013 Weight elements of Chevalley groups. Zbl 1206.20051Vavilov, N. A. 8 2009 Numerology of quadratic equations. Zbl 1206.20050Vavilov, N. A. 8 2009 Geometry of long root subgroups in Chevalley groups. Zbl 0662.20038Vavilov, N. A. 8 1988 Weight elements of Chevalley groups. Zbl 0727.20034Vavilov, N. A. 8 1988 Parabolic subgroups of Chevalley groups over a commutative ring. Zbl 0513.20029Vavilov, N. A. 8 1982 On subgroups of split orthogonal groups in even dimensions. Zbl 0476.20030Vavilov, N. A. 8 1981 Generation of relative commutator subgroups in Chevalley groups. II. Zbl 1481.20182Vavilov, Nikolai; Zhang, Zuhong 7 2020 Bruhat decomposition for long root tori in Chevalley groups. Zbl 0746.20024Vavilov, N. A.; Semenov, A. A. 7 1989 Gauss decomposition for Chevalley groups, revisited. Zbl 1261.20050Smolensky, A. V.; Sury, Balasubramanian; Vavilov, Nikolai A. 7 2012 Net subgroups of Chevalley groups. Zbl 0445.20026Vavilov, N. A.; Plotkin, E. B. 7 1979 Linear groups generated by one-parameter groups of one-dimensional transformations. Zbl 0679.20045Vavilov, N. A. 7 1989 Subgroups of the general symplectic group containing the group of diagonal matrices. Zbl 0529.20036Vavilov, N. A.; Dybkova, E. V. 7 1984 On the description of overgroups of \(E(m,R)\otimes E(n,R)\). Zbl 1183.20056Ananievsky, A. S.; Vavilov, N. A.; Sinchuk, S. S. 7 2009 On the parabolic congruence subgroups of linear groups. Zbl 0364.20057Vavilov, N. A. 7 1976 Basic reductions in the description of normal subgroups. Zbl 1312.20043Vavilov, N. A.; Stavrova, A. K. 7 2008 Net subgroups of Chevalley groups. Zbl 0485.20037Vavilov, N. A.; Plotkin, E. B. 7 1982 Some more exceptional numerology. Zbl 1215.20043Vavilov, N. A. 6 2010 Dennis-Vaserstein type decompositions. Zbl 1215.20049Vavilov, N. A.; Sinchuk, S. S. 6 2010 On parabolic subgroups of Chevalley groups of twisted type over a semi- local ring. Zbl 0445.20027Vavilov, N. A. 6 1979 Semisimple root elements and triples of unipotent root subgroups in Chevalley groups. Zbl 0711.20027Vavilov, N. A. 6 1989 The distribution of subgroups containing a group of block diagonal matrices in the general linear group over a ring. Zbl 0521.20033Borevich, Z. I.; Vavilov, N. A. 6 1982 Polyvector representations of \(\text{GL}_n\). Zbl 1125.20031Vavilov, N. A.; Perelman, E. Ya. 6 2006 Yet another variation on the theme of decomposition of transvections. Zbl 1175.20043Vavilov, N. A.; Kazakevich, V. G. 6 2008 On subgroups of the general linear group over a semi-local ring containing the group of diagonal matrices. Zbl 0461.20037Vavilov, N. A. 6 1981 Commutators of relative and unrelative elementary groups, revisited. Zbl 1472.20112Vavilov, N.; Zhang, Z. 6 2020 Net subgroups of Chevalley groups. II: The Gauss decomposition. Zbl 0499.20033Vavilov, N. A.; Plotkin, E. B. 6 1982 The intersection of two Bruhat cells. Zbl 1069.20036Vavilov, N. A.; Mitrofanov, M. Yu. 5 2001 Subgroups of the general linear group over a semilocal ring, containing the group of diagonal matrices. Zbl 0453.20040Borevich, Z. I.; Vavilov, N. A. 5 1980 Mutual arrangement of long and short root subgroups in a Chevalley group. Zbl 0673.20018Vavilov, N. A. 5 1989 On the subgroups of the full linear group over a commutative ring. Zbl 0521.20031Borevich, Z. I.; Vavilov, N. A. 5 1982 Parabolic factorizations of split classical groups. Zbl 1283.20057Vavilov, N. A.; Sinchuk, S. S. 5 2012 \(A_3\)-proof of structure theorems for Chevalley groups of types \(E_6\) and \(E_7\). II: Main lemma. Zbl 1278.20065Vavilov, N. A. 5 2012 Parabolic subgroups of the general linear group over a Dedekind domain of arithmetic type. Zbl 0416.20046Vavilov, N. A. 5 1977 Description of subgroups of the full linear group over a semilocal ring that contain the group of diagonal matrices. Zbl 0462.20042Vavilov, N. A. 5 1981 Subgroups of symplectic groups that contain a subsystem subgroup. Zbl 1312.20046Vavilov, N. A. 5 2008 Normal structure of the full linear group over a semilocal ring. Zbl 0485.20045Vavilov, N. A.; Kolotilina, L. Yu. 5 1982 Normalizer of the Chevalley group of type \(\mathrm{E}_7\). Zbl 1361.20034Vavilov, N. A.; Luzgarev, A. Yu. 4 2016 Long root semisimple elements in Chevalley groups. Zbl 0859.20035Vavilov, N. A.; Semenov, A. A. 4 1994 Presenting powers of augmentation ideals and Pfister forms. Zbl 0985.11016Bak, Anthony; Vavilov, Nikolai 4 2000 On subgroups of the general linear group over a Dedekind ring of arithmetic type. Zbl 0651.20049Vavilov, N. A. 4 1987 Bruhat decomposition of one-dimensional transformations. Zbl 0613.20028Vavilov, N. A. 4 1986 Subgroups of the general linear group over rings that satisfy stability conditions. Zbl 0702.20033Vavilov, N. A.; Stepanov, A. V. 4 1989 Subgroups of the general linear group over a semi-local ring containing the group of block-diagonal matrices. Zbl 0509.20035Vavilov, N. A. 4 1983 Bounded generation and commutator width of Chevalley groups: function case. Zbl 07712729Kunyavskiĭ, Boris; Plotkin, Eugene; Vavilov, Nikolai 2 2023 Toward the reverse decomposition of unipotents. II: The relative case. Zbl 1498.20126Vavilov, N. 1 2021 Generation of relative commutator subgroups in Chevalley groups. II. Zbl 1481.20182Vavilov, Nikolai; Zhang, Zuhong 7 2020 Commutators of relative and unrelative elementary groups, revisited. Zbl 1472.20112Vavilov, N.; Zhang, Z. 6 2020 Multiple commutators of elementary subgroups: end of the line. Zbl 1451.19004Vavilov, Nikolai; Zhang, Zuhong 3 2020 Commutators of congruence subgroups in the arithmetic case. Zbl 1443.13016Vavilov, N. 2 2020 Pairs of microweight tori in \(\mathrm{GL}_n\). Zbl 1477.20092Nesterov, Vladimir Viktorovich; Vavilov, Nikolaĭ Aleksandrovich 1 2020 Reshaping the metaphor of proof. Zbl 1436.00043Vavilov, Nikolai 4 2019 Unrelativized standard commutator formula. Zbl 1428.20033Vavilov, Nikolaĭ A. 4 2019 Towards the reverse decomposition of unipotents. Zbl 1472.20115Vavilov, N. A. 1 2019 The commutators of classical groups. Zbl 1393.20023Hazrat, R.; Vavilov, Nikolai; Zhang, Z. 9 2017 Multiple commutator formulas for unitary groups. Zbl 1403.20049Hazrat, R.; Vavilov, Nikolai; Zhang, Z. 9 2017 Generation of relative commutator subgroups in Chevalley groups. Zbl 1348.20055Hazrat, R.; Vavilov, N.; Zhang, Z. 11 2016 Normalizer of the Chevalley group of type \(\mathrm{E}_7\). Zbl 1361.20034Vavilov, N. A.; Luzgarev, A. Yu. 4 2016 Decomposition of unipotents for \(\mathrm{E}_6\) and \(\mathrm{E}_7\): 25 years after. Zbl 1367.20056Vavilov, Nikolai A. 3 2016 On Grothendieck-Serre’s conjecture concerning principal \(G\)-bundles over reductive group schemes: I. Zbl 1317.14102Panin, I.; Stavrova, A.; Vavilov, N. 22 2015 The yoga of commutators: further applications. Zbl 1316.20055Hazrat, R.; Stepanov, A. V.; Vavilov, N. A.; Zhang, Z. 10 2014 Commutator width in Chevalley groups. Zbl 1294.20059Hazrat, Roozbeh; Stepanov, Alexei; Vavilov, Nikolai; Zhang, Zuhong 26 2013 Relative commutator calculus in Chevalley groups. Zbl 1292.20053Hazrat, Roozbeh; Vavilov, Nikolai; Zhang, Zuhong 17 2013 Overgroups of subsystem subgroups in exceptional groups: levels. Zbl 1301.20043Vavilov, N. A.; Shchegolev, A. V. 9 2013 Linear groups over general rings. I: Generalities. Zbl 1278.20066Vavilov, N. A.; Stepanov, A. V. 8 2013 Long root tori in Chevalley groups. Zbl 1304.20062Vavilov, N. A.; Semenov, A. A. 3 2013 \(\mathrm{SL}_2\)-factorizations of Chevalley groups. Zbl 1278.20060Vavilov, N. A.; Kovach, E. I. 1 2013 Chevalley groups of type \(E_7\) in the 56-dimensional representation. Zbl 1306.20050Vavilov, N. A.; Luzgarev, A. Yu. 9 2012 Unitriangular factorizations of Chevalley groups. Zbl 1261.20051Vavilov, N. A.; Smolensky, A. V.; Sury, B. 8 2012 Gauss decomposition for Chevalley groups, revisited. Zbl 1261.20050Smolensky, A. V.; Sury, Balasubramanian; Vavilov, Nikolai A. 7 2012 Parabolic factorizations of split classical groups. Zbl 1283.20057Vavilov, N. A.; Sinchuk, S. S. 5 2012 \(A_3\)-proof of structure theorems for Chevalley groups of types \(E_6\) and \(E_7\). II: Main lemma. Zbl 1278.20065Vavilov, N. A. 5 2012 Overgroups of \(E(m,R)\otimes E(n,R)\). I: Levels and normalizers. Zbl 1278.20069Anan’evskiĭ, A. S.; Vavilov, N. A.; Sinchuk, S. S. 3 2012 The yoga of commutators. Zbl 1318.20049Hazrat, R.; Stepanov, A. V.; Vavilov, N. A.; Zhang, Z. 24 2011 On the length of commutators in Chevalley groups. Zbl 1262.20054Stepanov, Alexei; Vavilov, Nikolai 20 2011 Relative unitary commutator calculus, and applications. Zbl 1245.20064Hazrat, Roozbeh; Vavilov, Nikolai; Zhang, Zuhong 18 2011 On subgroups normalized by \(\mathrm{EO}(2l,R)\). Zbl 1273.20046Bakulin, S. V.; Vavilov, N. A. 2 2011 Relative subgroups in Chevalley groups. Zbl 1204.20066Hazrat, R.; Petrov, V.; Vavilov, N. 16 2010 Standard commutator formula, revisited. Zbl 1254.20038Vavilov, N. A.; Stepanov, A. V. 16 2010 More variations on the decomposition of transvections. Zbl 1215.20048Vavilov, N. A.; Kazakevich, V. G. 9 2010 Calculations in exceptional groups over rings. Zbl 1288.20063Luzgarev, A.; Stepanov, A.; Vavilov, N. 9 2010 Some more exceptional numerology. Zbl 1215.20043Vavilov, N. A. 6 2010 Dennis-Vaserstein type decompositions. Zbl 1215.20049Vavilov, N. A.; Sinchuk, S. S. 6 2010 The structure of isotropic reductive groups. Zbl 1459.20038Vavilov, N. A. 2 2010 Parabolic subgroups of \(\mathrm{SL}_n\) and \(\mathrm{Sp}_{2l}\) over a Dedekind ring of arithmetic type. Zbl 1215.20047Aleksandrov, A. V.; Vavilov, N. A. 1 2010 Bak’s work on the \(K\)-theory of rings. Zbl 1183.19001Hazrat, Roozbeh; Vavilov, Nikolai 44 2009 Localization-completion strikes again: relative \(K_1\) is nilpotent by Abelian. Zbl 1167.19002Bak, A.; Hazrat, R.; Vavilov, N. 33 2009 \(A_2\)-proof of structure theorems for Chevalley groups of type \(F_4\). Zbl 1206.20055Vavilov, N. A.; Nikolenko, S. I. 11 2009 Weight elements of Chevalley groups. Zbl 1206.20051Vavilov, N. A. 8 2009 Numerology of quadratic equations. Zbl 1206.20050Vavilov, N. A. 8 2009 On the description of overgroups of \(E(m,R)\otimes E(n,R)\). Zbl 1183.20056Ananievsky, A. S.; Vavilov, N. A.; Sinchuk, S. S. 7 2009 Decomposition of transvections for automorphisms. Zbl 1211.20043Vavilov, N. A.; Kazakevich, V. G. 3 2009 Overgroups of semisimple groups. Zbl 1322.20040Vavilov, N. A.; Stepanov, A. V. 27 2008 Standard commutator formula. Zbl 1147.20042Vavilov, N. A.; Stepanov, A. V. 24 2008 Normalizer of the Chevalley group of type \(E_6\). Zbl 1206.20054Vavilov, N. A.; Luzgarev, A. Yu. 10 2008 Can one see the signs of structure constants? Zbl 1203.20041Vavilov, N. A. 9 2008 Overgroups of \(\text{EO}(n,R)\). Zbl 1159.20024Vavilov, N. A.; Petrov, V. A. 8 2008 Basic reductions in the description of normal subgroups. Zbl 1312.20043Vavilov, N. A.; Stavrova, A. K. 7 2008 Yet another variation on the theme of decomposition of transvections. Zbl 1175.20043Vavilov, N. A.; Kazakevich, V. G. 6 2008 Subgroups of symplectic groups that contain a subsystem subgroup. Zbl 1312.20046Vavilov, N. A. 5 2008 Geometry of microweight tori. Zbl 1324.20026Vavilov, N. A.; Nesterov, V. V. 4 2008 Geometry of 1-tori in \(\text{GL}_n\). Zbl 1202.20054Vavilov, N. A. 1 2008 An \(A_3\)-proof of structure theorems for Chevalley groups of types \(E_6\) and \(E_7\). Zbl 1172.20034Vavilov, Nikolai 25 2007 Structure of Chevalley groups: the proof from The Book. Zbl 1162.20032Vavilov, N. A.; Gavrilovich, M. R.; Nikolenko, S. I. 27 2006 Chevalley group of type \(E_6\) in the 27-dimensional representation. Zbl 1124.20032Vavilov, N. A.; Luzgarev, A. Yu.; Pevzner, I. M. 22 2006 Polyvector representations of \(\text{GL}_n\). Zbl 1125.20031Vavilov, N. A.; Perelman, E. Ya. 6 2006 Orbits of subsystem stabilisers. Zbl 1144.20023Vavilov, N. A.; Kharchev, N. P. 2 2006 An \(A_2\)-proof of structure theorems for Chevalley groups of types \(E_6\) and \(E_7\). Zbl 1105.20039Vavilov, N. A.; Gavrilovich, M. R. 18 2005 Overgroups of elementary symplectic groups. Zbl 1075.20017Vavilov, N. A.; Petrov, V. A. 12 2004 \(K_{1}\) of Chevalley groups are nilpotent. Zbl 1012.19001Hazrat, Roozbeh; Vavilov, Nikolai 62 2003 Subgroups of split orthogonal groups. II. Zbl 1052.20030Vavilov, N. A. 1 2002 Subgroups of the spinor group that contain a split maximal torus. II. Zbl 1070.20057Vavilov, N. A. 1 2002 Do it yourself: the structure constants for Lie algebras of types \(E_l\). Zbl 1062.17004Vavilov, N. A. 22 2001 Subgroups of split orthogonal groups over a commutative ring. Zbl 1080.20046Vavilov, N. A. 11 2001 The intersection of two Bruhat cells. Zbl 1069.20036Vavilov, N. A.; Mitrofanov, M. Yu. 5 2001 Decomposition of transvections: A theme with variations. Zbl 0944.20031Stepanov, Alexei; Vavilov, Nikolai 71 2000 Structure of hyperbolic unitary groups. I: Elementary subgroups. Zbl 0963.20024Bak, Anthony; Vavilov, Nikolai 67 2000 A third look at weight diagrams. Zbl 1016.20029Vavilov, Nikolai 45 2000 On the overgroups of \(\text{EO}(2l,R)\). Zbl 1069.20040Vavilov, N. A.; Petrov, V. A. 15 2000 Presenting powers of augmentation ideals and Pfister forms. Zbl 0985.11016Bak, Anthony; Vavilov, Nikolai 4 2000 Visual basic representations: An atlas. Zbl 0957.17006Plotkin, Eugene; Semenov, Andrei; Vavilov, Nikolai 44 1998 Chevalley groups over commutative rings. I: Elementary calculations. Zbl 0861.20044Vavilov, Nikolai; Plotkin, Eugene 68 1996 \((2,3)\)-generation of \(\text{SL}(n,q)\). II: Cases \(n\geq 8\). Zbl 0847.20043Di Martino, Lino; Vavilov, Nikolai 16 1996 On the lattice of subgroups of Chevalley groups containing a split maximal torus. Zbl 0857.20023Harebov, Alan; Vavilov, Nikolai 10 1996 Normality for elementary subgroup functors. Zbl 0857.20028Bak, Anthony; Vavilov, Nikolai 36 1995 Intermediate subgroups in Chevalley groups. Zbl 0879.20020Vavilov, Nikolai 26 1995 Unipotent elements in subgroups which contain a split maximal torus. Zbl 0865.20030Vavilov, Nikolai 3 1995 \((2,3)\)-generation of \(SL(n,q)\). I: Cases \(n=5,6,7\). Zbl 0805.20038Di Martino, Lino; Vavilov, Nikolai 20 1994 Long root semisimple elements in Chevalley groups. Zbl 0859.20035Vavilov, N. A.; Semenov, A. A. 4 1994 Subgroups of Chevalley groups containing a maximal torus. Zbl 0796.20034Vavilov, N. A. 2 1993 On subgroups of the general symplectic group over a commutative ring. Zbl 0900.19002Vavilov, N. A. 2 1993 Unipotent elements in subgroups of extended Chevalley groups containing a split maximal torus. Zbl 0830.20069Vavilov, N. A. 2 1993 Structure of Chevalley groups over commutative rings. Zbl 0799.20042Vavilov, Nikolai A. 58 1991 Subgroups of a spinor group containing a maximal split torus. I. Zbl 0779.20024Vavilov, N. A. 1 1991 On subgroups of splittable classical groups. Zbl 0723.20028Vavilov, N. A. 13 1990 A note on the subnormal structure of general linear groups. Zbl 0701.20025Vavilov, N. A. 12 1990 On subgroups of split classical groups. Zbl 0741.20034Vavilov, N. A. 8 1990 Computations in Chevalley groups over commutative rings. Zbl 0795.20028Vavilov, N. A.; Plotkin, E. B.; Stepanov, A. V. 23 1989 Bruhat decomposition for long root tori in Chevalley groups. Zbl 0746.20024Vavilov, N. A.; Semenov, A. A. 7 1989 Linear groups generated by one-parameter groups of one-dimensional transformations. Zbl 0679.20045Vavilov, N. A. 7 1989 Semisimple root elements and triples of unipotent root subgroups in Chevalley groups. Zbl 0711.20027Vavilov, N. A. 6 1989 Mutual arrangement of long and short root subgroups in a Chevalley group. Zbl 0673.20018Vavilov, N. A. 5 1989 Subgroups of the general linear group over rings that satisfy stability conditions. Zbl 0702.20033Vavilov, N. A.; Stepanov, A. V. 4 1989 On subgroups of the general linear group over a ring satisfying stability conditions. Zbl 0692.20034Vavilov, N. A.; Stepanov, A. V. 3 1989 ...and 59 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 212 Authors 87 Vavilov, Nikolaĭ Aleksandrovich 20 Stepanov, Alexeĭ Vladimirovich 16 Zhang, Zuhong 13 Hazrat, Roozbeh 11 Bunina, Elena Igor’evna 10 Luzgarev, A. Yu. 10 Panin, Ivan A. 9 Bashkirov, Evgenii L. 9 Gvozdevsky, Pavel 9 Plotkin, Eugene 9 Sinchuk, Sergeĭ Sergeevich 9 Stavrova, Anastasia K. 8 Pevzner, Igor’ M. 7 Preusser, Raimund 7 Rao, Ravi A. 6 Bak, Anthony 6 Borevich, Zenon Ivanovich 6 Vsemirnov, Maxim 5 Basu, Rabeya 5 Smolensky, Andrei 5 Vaserstein, Leonid N. 4 Dybkova, E. V. 4 Koĭbaev, Vladimir Amurkhanovich 4 Nuzhin, Yakov Nifant’evich 4 You, Hong 3 Chen, Yu 3 Di Martino, Lino 3 Fedorov, Roman M. 3 Garibaldi, Skip 3 Gordeev, Nikolai L. 3 Hoi, Tran Ngoc 3 Hołubowski, Waldemar 3 Jose, Selby 3 Kazakevich, V. G. 3 Kunyavskiĭ, Boris Èmmanuilovich 3 Lavrenov, Andrei V. 3 Lubkov, Roman A. 3 Menal, Pere 3 Nesterov, Vladimir Viktorovich 3 Nhat, Nguyen Huu Tri 3 Petrov, Viktor 3 Shchegolev, A. V. 3 Tamburini, Maria Chiara 3 Tang, Guoping 3 Vasilyev, V. L. 3 Zalesski, Alexandre Efimovich 2 Ambily, Ambattu Asokan 2 Anan’evskii, A. S. 2 Bui Xuan Hai 2 Česnavičius, Kęstutis 2 Chang, Shan 2 de Graaf, Willem Adriaan 2 Ellers, Erich Werner 2 Garonzi, Martino 2 Gavrilovich, Mikhaĭl R. 2 Gupta, Chander Kanta 2 Khanna, Reema 2 Kolotilina, Lily Yu. 2 Levchuk, Vladimir M. 2 Levy, Dan 2 Pellegrini, Marco Antonio 2 Röhrle, Gerhard E. 2 Semenov, Alexey A. 2 Semenov, N. S. 2 Słowik, Roksana 2 Voronetsky, E. Yu. 2 Voronetsky, Egor 2 Wendt, Matthias 2 Yu, Weibo 2 Zhou, Xuemei 1 Aleksandrov, A. V. 1 Ali, Faryad 1 Apte, Himanee 1 Aschbacher, Michael George 1 Asok, Aravind 1 Atamanova, M. M. 1 Avdeev, Roman S. 1 Azad, Hassan 1 Bakulin, S. V. 1 Al-Ali Bani-Ata, Mashhour 1 Bardini, Carla 1 Batalkin, K. O. 1 Baur, Karin 1 Beauchard, Karine 1 Beth, Thomas 1 Biswas, Dipnit 1 Biswas, Indranil 1 Bovdi, Victor A. 1 Carberry, Emma 1 Carbone, Lisa J. 1 Carr, Michael 1 Cazzola, Marina 1 Chattopadhyay, Pratyusha 1 Chernousov, Vladimir I. 1 Cupit-Foutou, Stéphanie 1 Das, Mrinal Kanti 1 Dashkova, Olga Yur’evna 1 Dietrich, Heiko 1 Distler, Jacques 1 Dokuchaev, Mikhailo ...and 112 more Authors all top 5 Cited in 78 Serials 68 Journal of Mathematical Sciences (New York) 41 St. Petersburg Mathematical Journal 27 Journal of Algebra 27 Journal of Soviet Mathematics 21 Communications in Algebra 14 Journal of Pure and Applied Algebra 8 Journal of \(K\)-Theory 7 Vestnik St. Petersburg University. 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Mathematics & Physics all top 5 Cited in 25 Fields 287 Group theory and generalizations (20-XX) 52 \(K\)-theory (19-XX) 42 Algebraic geometry (14-XX) 38 Nonassociative rings and algebras (17-XX) 22 Commutative algebra (13-XX) 14 Associative rings and algebras (16-XX) 13 Number theory (11-XX) 12 Linear and multilinear algebra; matrix theory (15-XX) 7 History and biography (01-XX) 5 Mathematical logic and foundations (03-XX) 5 Topological groups, Lie groups (22-XX) 4 Category theory; homological algebra (18-XX) 3 Algebraic topology (55-XX) 3 Manifolds and cell complexes (57-XX) 2 General and overarching topics; collections (00-XX) 2 Combinatorics (05-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Quantum theory (81-XX) 1 General algebraic systems (08-XX) 1 Functional analysis (46-XX) 1 Geometry (51-XX) 1 Differential geometry (53-XX) 1 Computer science (68-XX) 1 Mechanics of deformable solids (74-XX) 1 Mathematics education (97-XX) Citations by Year