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Mat. Sb. (N.S.), 1973, Volume 91(133), Number 3(7), Pages 445–470 (Mi msb3308)  

This article is cited in 22 scientific papers (total in 22 papers)

The structure of classical arithmetic groups of rank greater than one

L. N. Vaserstein


Abstract: We study the structure and describe the normal subgroups of the classical arithmetic groups of relative rank greater than one.
Bibliography: 32 titles.

Full text: PDF file (2857 kB)
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English version:
Mathematics of the USSR-Sbornik, 1973, 20:3, 465–492

Bibliographic databases:

UDC: 519.46
MSC: Primary 10C30, 20H05; Secondary 20H25
Received: 27.05.1971

Citation: L. N. Vaserstein, “The structure of classical arithmetic groups of rank greater than one”, Mat. Sb. (N.S.), 91(133):3(7) (1973), 445–470; Math. USSR-Sb., 20:3 (1973), 465–492

Citation in format AMSBIB
\Bibitem{Vas73}
\by L.~N.~Vaserstein
\paper The structure of classical arithmetic groups of rank greater than one
\jour Mat. Sb. (N.S.)
\yr 1973
\vol 91(133)
\issue 3(7)
\pages 445--470
\mathnet{http://mi.mathnet.ru/msb3308}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=349864}
\zmath{https://zbmath.org/?q=an:0277.14018}
\transl
\jour Math. USSR-Sb.
\yr 1973
\vol 20
\issue 3
\pages 465--492
\crossref{https://doi.org/10.1070/SM1973v020n03ABEH001885}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. L. N. Vaserstein, “Stabilization for classical groups over rings”, Math. USSR-Sb., 22:2 (1974), 271–303  mathnet  crossref  mathscinet  zmath
    2. L. N. Vaserstein, A. A. Suslin, “Serre's problem on projective modules over polynomial rings, and algebraic $K$-theory”, Math. USSR-Izv., 10:5 (1976), 937–1001  mathnet  crossref  mathscinet  zmath
    3. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    4. G. A. Margulis, “Finiteness of quotient groups of discrete subgroups”, Funct. Anal. Appl., 13:3 (1979), 178–187  mathnet  crossref  mathscinet  zmath
    5. Anthony Bak, Ulf Rehmann, “The congruence subgroup and metaplectic problems for SLn ⩾ 2 of division algebras”, Journal of Algebra, 78:2 (1982), 475  crossref  mathscinet  zmath
    6. Bruce Magurn, Robert Oliver, Leonid Vaserstein, “Units in Whitehead groups of finite groups”, Journal of Algebra, 84:2 (1983), 324  crossref  mathscinet  zmath
    7. L.N. Vaserstein, “On arithmetic subgroups of simple algebraic groups”, Linear Algebra and its Applications, 72 (1985), 93  crossref  mathscinet  zmath
    8. Ashwani K. Bhandari, “On the generators of subgroups of unit groups of group rings”, Bol Soc Bras Mat, 20:2 (1990), 87  crossref  mathscinet  zmath
    9. O. I. Tavgen', “Bounded generation of Chevalley groups over rings of algebraic $S$-integers”, Math. USSR-Izv., 36:1 (1991), 101–128  mathnet  crossref  mathscinet  zmath  adsnasa
    10. Donald G. James, “Generators for orthogonal groups of unimodular lattices”, Linear Algebra and its Applications, 157 (1991), 101  crossref  mathscinet  zmath
    11. Jürgen Ritter, Sudarshan K Sehgal, “Construction of units in group rings of monomial and symmetric groups”, Journal of Algebra, 142:2 (1991), 511  crossref  mathscinet
    12. Eric Jespers, Guilherme Leal, “Generators of large subgroups of the unit group of integral group rings”, manuscripta math, 78:1 (1993), 303  crossref  mathscinet  zmath  isi
    13. Fritz Grunewald, Jens Mennicke, Leonid Vaserstein, “On the groups SL2(ℤ[x]) and SL2(k[x, y])”, Isr J Math, 86:1-3 (1994), 157  crossref  mathscinet  zmath  isi
    14. Eric Jespers, G. Leal, “Units of integral group rings of Hamiltonian groups*”, Communications in Algebra, 23:2 (1995), 623  crossref  mathscinet  zmath
    15. A. Katok, J. Lewis, “Global rigidity results for lattice actions on tori and new examples of volume-preserving actions”, Isr J Math, 93:1 (1996), 253  crossref  mathscinet  zmath  isi
    16. Eric Jespers, C.Polcino Milies, “Units of group rings”, Journal of Pure and Applied Algebra, 107:2-3 (1996), 233  crossref  mathscinet  zmath
    17. Hee Oh, “Discrete Subgroups Generated by Lattices in Opposite Horospherical Subgroups”, Journal of Algebra, 203:2 (1998), 621  crossref  mathscinet  zmath
    18. M. S. Raghunathan, “The congruence subgroup problem”, Proc Math Sci, 114:4 (2004), 299  crossref  mathscinet  zmath
    19. ANN DOOMS, “UNITARY UNITS IN INTEGRAL GROUP RINGS”, J. Algebra Appl, 05:01 (2006), 43  crossref  mathscinet
    20. Kenichi Fujiwara, “Refined Kirby calculus for three-manifolds of first homology groups of odd prime orders”, Topology and its Applications, 155:13 (2008), 1382  crossref  mathscinet  zmath
    21. T. N. Venkataramana, “Monodromy of cyclic coverings of the projective line”, Invent. math, 2013  crossref  mathscinet
    22. T. N. Venkataramana, “Image of the Burau representation at d-th roots of unity”, Ann. Math, 179:3 (2014), 1041  crossref  mathscinet  zmath
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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