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Zap. Nauchn. Sem. POMI, 2011, Volume 394, Pages 33–139 (Mi znsl4630)  

This article is cited in 2 scientific papers (total in 2 papers)

Linear groups over general rings. I. Generalities

N. A. Vavilova, A. V. Stepanovba

a Saint-Petersburg State University, Saint-Petersburg, Russia
b Abdus Salam School of Mathematical Sciences, Lahore, Pakistan

Abstract: 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 formulae, finiteness and stability conditions, stability and pre-stability theorems, nilpotency of $\mathrm K_1$, centrality of $\mathrm K_2$, automorphism and homomorphisms, etc. This first part covers background material such as one-sided inverses, elementary transformations, definitions of obvious subgroups, Bruhat and Gauss decompositions, relative subgroups, finitary phenomens, and transvections.

Key words and phrases: linear groups, general linear group, associative rings, one-sided inverses, weakly finite rings, IBN rings, elementary transvections, linear transvections, congruence subgroups, elementary subgroups, Bruhat decomposition, Gauss decomposition, parabolic subgroups, group of finitary matrices, Whitehead type lemmas.

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English version:
Journal of Mathematical Sciences (New York), 2013, 188:5, 490–550

Bibliographic databases:

Document Type: Article
UDC: 512.5
Received: 17.08.2011

Citation: N. A. Vavilov, A. V. Stepanov, “Linear groups over general rings. I. Generalities”, Problems in the theory of representations of algebras and groups. Part 22, Zap. Nauchn. Sem. POMI, 394, POMI, St. Petersburg, 2011, 33–139; J. Math. Sci. (N. Y.), 188:5 (2013), 490–550

Citation in format AMSBIB
\Bibitem{VavSte11}
\by N.~A.~Vavilov, A.~V.~Stepanov
\paper Linear groups over general rings.~I. Generalities
\inbook Problems in the theory of representations of algebras and groups. Part~22
\serial Zap. Nauchn. Sem. POMI
\yr 2011
\vol 394
\pages 33--139
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl4630}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2870172}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 5
\pages 490--550
\crossref{https://doi.org/10.1007/s10958-013-1146-7}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884413693}


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    This publication is cited in the following articles:
    1. J. Math. Sci. (N. Y.), 200:6 (2014), 742–768  mathnet  crossref
    2. E. Yu. Voronetskii, “Normalizatory elementarnykh nadgrupp $\mathrm{Ep}(2,A)$”, Voprosy teorii predstavlenii algebr i grupp. 30, Zap. nauchn. sem. POMI, 452, POMI, SPb., 2016, 32–51  mathnet  mathscinet
  • Записки научных семинаров ПОМИ
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