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Izv. Akad. Nauk SSSR Ser. Mat., 1969, Volume 33, Issue 6, Pages 1211–1219 (Mi izv2220)  

This article is cited in 31 scientific papers (total in 32 papers)

The problem of strong approximation and the Kneser–Tits conjecture for algebraic groups

V. P. Platonov


Abstract: We conclude an investigation of the problem of strong approximation in algebraic groups. A basic role is played by the proof of the Kneser–Tits conjecture concerning simple, simply connected groups over locally compact fields.

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English version:
Mathematics of the USSR-Izvestiya, 1969, 3:6, 1139–1147

Bibliographic databases:

UDC: 513.6
MSC: 22Dxx, 20C11
Received: 05.05.1969

Citation: V. P. Platonov, “The problem of strong approximation and the Kneser–Tits conjecture for algebraic groups”, Izv. Akad. Nauk SSSR Ser. Mat., 33:6 (1969), 1211–1219; Math. USSR-Izv., 3:6 (1969), 1139–1147

Citation in format AMSBIB
\Bibitem{Pla69}
\by V.~P.~Platonov
\paper The problem of strong approximation and the Kneser--Tits conjecture for algebraic groups
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1969
\vol 33
\issue 6
\pages 1211--1219
\mathnet{http://mi.mathnet.ru/izv2220}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=258839}
\zmath{https://zbmath.org/?q=an:0217.36301}
\transl
\jour Math. USSR-Izv.
\yr 1969
\vol 3
\issue 6
\pages 1139--1147
\crossref{https://doi.org/10.1070/IM1969v003n06ABEH000838}


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    Addendum

    This publication is cited in the following articles:
    1. V. P. Platonov, “Addendum to the paper “The problem of strong approximation and the Kneser–Tits conjecture for algebraic groups””, Math. USSR-Izv., 4:4 (1970), 784–786  mathnet  crossref  mathscinet  zmath
    2. V. I. Yanchevskii, “Simple algebras with involution, and unitary groups”, Math. USSR-Sb., 22:3 (1974), 372–385  mathnet  crossref  mathscinet  zmath
    3. G. A. Margulis, “Arithmetic properties of discrete subgroups”, Russian Math. Surveys, 29:1 (1974), 107–156  mathnet  crossref  mathscinet  zmath
    4. M. S. Raghunathan, “On the congruence subgroup problem”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 46:1 (1976), 107  crossref  mathscinet  zmath
    5. I. V. Cherednik, “Towers of algebraic curves uniformized by discrete subgroups of $PGL_2(k_w)\times E$”, Math. USSR-Sb., 28:2 (1976), 187–215  mathnet  crossref  mathscinet  zmath  isi
    6. I. V. Cherednik, “Uniformization of algebraic curves by discrete arithmetic subgroups of $PGL_2(k_w)$ with compact quotients”, Math. USSR-Sb., 29:1 (1976), 55–78  mathnet  crossref  mathscinet  zmath  isi
    7. V. P. Platonov, “The Tannaka–Artin problem and reduced $K$-theory”, Math. USSR-Izv., 10:2 (1976), 211–243  mathnet  crossref  mathscinet  zmath
    8. A. A. Bondarenko, “On the classification of maximal arithmetic subgroups in split groups”, Math. USSR-Sb., 31:2 (1977), 135–150  mathnet  crossref  mathscinet  zmath  isi
    9. G. A. Margulis, “Cobounded subgroups of algebraic groups over local fields”, Funct. Anal. Appl., 11:2 (1977), 119–128  mathnet  crossref  mathscinet  zmath
    10. J. Rohlfs, “Arithmetisch definierte Gruppen mit Galoisoperation”, Invent math, 48:2 (1978), 185  crossref  mathscinet  zmath  adsnasa
    11. V. I. Yanchevskii, “Reduced unitary $K$-theory and division rings over discretely valued Hensel fields”, Math. USSR-Izv., 13:1 (1979), 175–213  mathnet  crossref  mathscinet  zmath  isi
    12. V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk, “Class numbers and groups of algebraic groups”, Math. USSR-Izv., 14:3 (1980), 547–569  mathnet  crossref  mathscinet  zmath  isi
    13. G. A. Margulis, “Finiteness of quotient groups of discrete subgroups”, Funct. Anal. Appl., 13:3 (1979), 178–187  mathnet  crossref  mathscinet  zmath
    14. V. P. Platonov, A. A. Bondarenko, A. S. Rapinchuk, “Class numbers and groups of algebraic groups. II”, Math. USSR-Izv., 16:2 (1981), 357–372  mathnet  crossref  mathscinet  zmath  isi
    15. A. E. Zalesskii, “Linear groups”, Russian Math. Surveys, 36:5 (1981), 63–128  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. A. S. Rapinchuk, “Class numbers in the genus of quadratic forms, and algebraic groups”, Math. USSR-Izv., 19:1 (1982), 79–93  mathnet  crossref  mathscinet  zmath
    17. V. P. Platonov, “The arithmetic theory of algebraic groups”, Russian Math. Surveys, 37:3 (1982), 1–62  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    18. Gopal Prasad, M. S. Raghunathan, “On the Kneser-Tits problem”, Comment Math Helv, 60:1 (1985), 107  crossref  mathscinet  zmath  isi
    19. A. A. Bondarenko, “Classification of the maximal arithmetic subgroups of indefinite orthogonal groups of type $(B_l)$”, Math. USSR-Sb., 55:1 (1986), 71–89  mathnet  crossref  mathscinet  zmath
    20. Fritz Grunewald, Daniel Segal, “Decision problems concerning S-arithmetic groups”, J. symb. log, 50:03 (1985), 743  crossref
    21. A. S. Rapinchuk, “Multiplicative arithmetic of division algebras over number fields, and the metaplectic problem”, Math. USSR-Izv., 31:2 (1988), 349–379  mathnet  crossref  mathscinet  zmath
    22. A. P. Monastyrnyi, V. I. Yanchevskii, “Whitehead groups of spinor groups”, Math. USSR-Izv., 36:1 (1991), 61–100  mathnet  crossref  mathscinet  zmath  adsnasa
    23. G. M. Tomanov, “On the structure of division algebras of index $2^m$”, Russian Math. Surveys, 45:6 (1990), 170–172  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    24. B Sury, “Congruence subgroup problem for anisotropic groups over semilocal rings”, Proc Math Sci, 101:2 (1991), 87  crossref  mathscinet  zmath
    25. G. M. Tomanov, “On the group of reduced norm 1 group of a division algebra over a global field”, Math. USSR-Izv., 39:1 (1992), 895–904  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    26. V. P. Platonov, A. S. Rapinchuk, “Abstract properties of $S$-arithmetic groups and the congruence s problem”, Russian Acad. Sci. Izv. Math., 40:3 (1993), 455–476  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    27. G. A. Margulis, G. M. Tomanov, “Measure rigidity for almost linear groups and its applications”, J Anal Math, 69:1 (1996), 25  crossref  mathscinet  zmath  isi
    28. MASANORI MORISHITA, TAKAO WATANABE, “ON S-HARDY–LITTLEWOOD HOMOGENEOUS SPACES”, Int. J. Math, 09:06 (1998), 723  crossref
    29. Marcus Sautoy, “Countingp-groups and nilpotent groups”, Publications Mathématiques de l’Institut des Hautes Études Scientifiques, 92:1 (2000), 63  crossref  zmath
    30. S. I. Adian, E. I. Zel'manov, G. A. Margulis, S. P. Novikov, A. S. Rapinchuk, L. D. Faddeev, V. I. Yanchevskii, “Vladimir Petrovich Platonov (on his 60th birthday)”, Russian Math. Surveys, 55:3 (2000), 601–610  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    31. M. S. Raghunathan, “The congruence subgroup problem”, Proc Math Sci, 114:4 (2004), 299  crossref  mathscinet  zmath
    32. Proc. Steklov Inst. Math., 292 (2016), 216–246  mathnet  crossref  crossref  mathscinet  isi  elib
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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