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

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.

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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

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
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
3. L. N. Vaserstein, “Foundations of algebraic $K$-theory”, Russian Math. Surveys, 31:4 (1976), 89–156
4. G. A. Margulis, “Finiteness of quotient groups of discrete subgroups”, Funct. Anal. Appl., 13:3 (1979), 178–187
5. Anthony Bak, Ulf Rehmann, “The congruence subgroup and metaplectic problems for SLn ⩾ 2 of division algebras”, Journal of Algebra, 78:2 (1982), 475
6. Bruce Magurn, Robert Oliver, Leonid Vaserstein, “Units in Whitehead groups of finite groups”, Journal of Algebra, 84:2 (1983), 324
7. L.N. Vaserstein, “On arithmetic subgroups of simple algebraic groups”, Linear Algebra and its Applications, 72 (1985), 93
8. Ashwani K. Bhandari, “On the generators of subgroups of unit groups of group rings”, Bol Soc Bras Mat, 20:2 (1990), 87
9. O. I. Tavgen', “Bounded generation of Chevalley groups over rings of algebraic $S$-integers”, Math. USSR-Izv., 36:1 (1991), 101–128
10. Donald G. James, “Generators for orthogonal groups of unimodular lattices”, Linear Algebra and its Applications, 157 (1991), 101
11. Jürgen Ritter, Sudarshan K Sehgal, “Construction of units in group rings of monomial and symmetric groups”, Journal of Algebra, 142:2 (1991), 511
12. Eric Jespers, Guilherme Leal, “Generators of large subgroups of the unit group of integral group rings”, manuscripta math, 78:1 (1993), 303
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
14. Eric Jespers, G. Leal, “Units of integral group rings of Hamiltonian groups*”, Communications in Algebra, 23:2 (1995), 623
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
16. Eric Jespers, C.Polcino Milies, “Units of group rings”, Journal of Pure and Applied Algebra, 107:2-3 (1996), 233
17. Hee Oh, “Discrete Subgroups Generated by Lattices in Opposite Horospherical Subgroups”, Journal of Algebra, 203:2 (1998), 621
18. M. S. Raghunathan, “The congruence subgroup problem”, Proc Math Sci, 114:4 (2004), 299
19. ANN DOOMS, “UNITARY UNITS IN INTEGRAL GROUP RINGS”, J. Algebra Appl, 05:01 (2006), 43
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
21. T. N. Venkataramana, “Monodromy of cyclic coverings of the projective line”, Invent. math, 2013
22. T. N. Venkataramana, “Image of the Burau representation at d-th roots of unity”, Ann. Math, 179:3 (2014), 1041
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