Linear groups over general rings. I. Generalities

N. A. Vavilov; A. V. Stepanov

Linear groups over general rings. I. Generalities

N. A. Vavilov ; A. V. Stepanov

Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 33-139 Cet article a éte moissonné depuis la source Math-Net.Ru

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Résumé

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.

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@article{ZNSL_2011_394_a2,
     author = {N. A. Vavilov and A. V. Stepanov},
     title = {Linear groups over general {rings.~I.} {Generalities}},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {33--139},
     year = {2011},
     volume = {394},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a2/}
}

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N. A. Vavilov; A. V. Stepanov. Linear groups over general rings. I. Generalities. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 22, Tome 394 (2011), pp. 33-139. http://geodesic.mathdoc.fr/item/ZNSL_2011_394_a2/

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