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Mat. Sb. (N.S.), 1974, Volume 93(135), Number 2, Pages 268–295 (Mi msb2973)  

This article is cited in 14 scientific papers (total in 14 papers)

Stabilization for classical groups over rings

L. N. Vaserstein


Abstract: The main goal of this paper is to prove theorems about stabilization for groups of automorphisms of modules over rings and modules with quadratic forms over rings with involutions, which allow us to describe the structure of all the classical arithmetic groups of rank greater than one. The presentation is made in such generality that our results generalize and strengthen many previously known results about transitivity and cancellation, about normal subgroups, etc.
Bibliography: 14 titles.

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English version:
Mathematics of the USSR-Sbornik, 1974, 22:2, 271–303

Bibliographic databases:

UDC: 519.46
MSC: Primary 13C10, 18F25, 20G35; Secondary 10C30, 16A50
Received: 01.06.1971 and 01.10.1973

Citation: L. N. Vaserstein, “Stabilization for classical groups over rings”, Mat. Sb. (N.S.), 93(135):2 (1974), 268–295; Math. USSR-Sb., 22:2 (1974), 271–303

Citation in format AMSBIB
\Bibitem{Vas74}
\by L.~N.~Vaserstein
\paper Stabilization for classical groups over rings
\jour Mat. Sb. (N.S.)
\yr 1974
\vol 93(135)
\issue 2
\pages 268--295
\mathnet{http://mi.mathnet.ru/msb2973}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=338208}
\zmath{https://zbmath.org/?q=an:0287.18015}
\transl
\jour Math. USSR-Sb.
\yr 1974
\vol 22
\issue 2
\pages 271--303
\crossref{https://doi.org/10.1070/SM1974v022n02ABEH001693}


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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, 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
    2. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156  mathnet  crossref  mathscinet  zmath
    3. L.N. Vaserstein, “Normal subgroups of the general linear groups over Banach algebras”, Journal of Pure and Applied Algebra, 41 (1986), 99  crossref
    4. L.N. Vaserstein, B.A. Magurnt, “Prestabilization for K1 of Banach algebras”, Linear Algebra and its Applications, 95 (1987), 69  crossref
    5. Vaserstein L., “Computation of K1 via Mennicke Symbols”, Commun. Algebr., 15:3 (1987), 611–656  crossref  isi
    6. Grunewald F. Mennicke J. Vaserstein L., “On Symplectic Groups Over Polynomial-Rings”, Math. Z., 206:1 (1991), 35–56  crossref  isi
    7. V. I. Kopeiko, “On the structure of the symplectic group of polynomial rings over regular rings of dimension $\le 1$”, Russian Math. Surveys, 47:4 (1992), 210–211  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. Nikolai Vavilov, Eugene Plotkin, “Chevalley groups over commutative rings: I. Elementary calculations”, Acta Appl Math, 45:1 (1996), 73  crossref  mathscinet  zmath  isi  elib
    9. Hong You, Shengkui Ye, “Prestability for quadratic of Λ-1-fold stable rings”, Journal of Algebra, 319:5 (2008), 2072  crossref
    10. N. A. Vavilov, S. S. Sinchuk, “Dennis–Vaserstein type decompositions”, J. Math. Sci. (N. Y.), 171:3 (2010), 331–337  mathnet  crossref
    11. N. A. Vavilov, S. S. Sinchuk, “Parabolic factorizations of split classical groups”, St. Petersburg Math. J., 23:4 (2012), 637–657  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    12. N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, J. Math. Sci. (N. Y.), 188:5 (2013), 490–550  mathnet  crossref  mathscinet
    13. K. B. Tsvetkov, “Parabolic factorization for a matrix ring”, J. Math. Sci. (N. Y.), 202:3 (2014), 479–484  mathnet  crossref  mathscinet
    14. J. Math. Sci. (N. Y.), 232:5 (2018), 591–609  mathnet  crossref  mathscinet
  • Математический сборник (новая серия) - 1964–1988 Sbornik: Mathematics (from 1967)
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