Linear groups over general rings. I: Generalities. (English. Russian original) Zbl 1278.20066
J. Math. Sci., New York 188, No. 5, 490-550 (2013); translation from Zap. Nauchn. Semin. POMI 394, 33-139 (2011).
This paper is the first part of a systematic survey on the structure of classical groups over general rings. It covers background material such as one-sided inverses, elementary transformations, definitions of obvious subgroups, Bruhat and Gauss decompositions, relative subgroups, finitary phenomena, and transvections.
Reviewer: L. N. Vaserstein (University Park)
MSC:
| 20G35 | Linear algebraic groups over adèles and other rings and schemes |
| 20H25 | Other matrix groups over rings |
| 20-02 | Research exposition (monographs, survey articles) pertaining to group theory |
| 20F05 | Generators, relations, and presentations of groups |
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