Linear groups over general rings. I. Generalities

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.