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JOURNALS // Zapiski Nauchnykh Seminarov POMI // Archive

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

This article is cited in 16 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.

UDC: 512.5

Received: 17.08.2011


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

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