Linear groups over general rings. I. Generalities

被引：0
作者：
Vavilov N.A. [1 ]
Stepanov A.V. [1 ,2 ]
机构：
[1] St. Petersburg State University, St. Petersburg
[2] Abdus Salam School of mathematical Sciences, Lahore
来源：
Journal of Mathematical Sciences | 2013年 / 188卷 / 5期
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D O I：
10.1007/s10958-013-1146-7
中图分类号：
学科分类号：
摘要：
This paper is the first part of a systematic survey on the structure of classical groups over general rings. We intend to cover various proofs of the main structure theorems, commutator formulas, finiteness and stability conditions, stability and prestability theorems, the nilpotency of K1, the centrality of K2, automorphisms and homomorphisms, etc. This first part covers background material such as one-sided inverse, elementary transformations, definitions of obvious subgroups, Bruhat and Gauß decompositions, relative subgroups, finitary phenomena, and transvections. Bibliography: 674 titles. © 2013 Springer Science+Business Media New York.
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页码：490 / 550
页数：60
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  • [1] Abe, E., Automorphisms of Chevalley groups over commutative rings (1993) Algebra Analiz, 5 (2), pp. 74-90
  • [2] Artin, E., (1969) Geometrieal Algebra [Russian Translation], , Moscow: Nauka
  • [3] Atkarskaya, A.S., (2009) Automorphisms of the group GLn (R), n ≥ 4, over an associative graded ring, , team paper, Moscow State University
  • [4] Bardakov, V.G., On factorization of automorphisms of free modules into prime factors (1995) Izv. RAN, Ser. Mat., 59 (2), pp. 109-128
  • [5] Bass, H., (1973) Algebraic K-Theory [Russian Translation], , Moscow: Mir
  • [6] Bass, H., Milnor, J., Serre, J.-P., Solution of the congruence problem for SLn (n ≥ 3) and Sp2n (n ≥ 2) (1970) Matematika, 14 (6), pp. 64-128. , 15, No. 1, 44-60 (1971)
  • [7] Bondarko, V.M., On the similarity of matrices over residue rings (1976) Collection of Mathematical Works, pp. 275-277. , Naukova Dumka, Kiev
  • [8] Borewicz, Z.I., Vavilov, N.A., Arrangement of subgroups that contain the group of block diagonal matrices in the general linear group over a ring (1982) Matematika, Izv. VUZ'ov, 11, pp. 12-16
  • [9] Borewicz, Z.I., Vavilov, N.A., On the definition of a net subgroup (1983) Zap. Nauchn. Semin. LOMI, 132, pp. 26-33
  • [10] Borewicz, Z.I., Vavilov, N.A., Arrangernent of subgroups in the general linear group over a commutative ring (1984) Trudy Mat. Inst. AN SSSR, 165, pp. 24-42
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