caa a22 4500 60552596X CHVBK 20210128100801.0 cr unu---uuuuu 210128e20150901xx s 000 0 eng 10.1007/s10958-015-2518-y doi (NATIONALLICENCE)springer-10.1007/s10958-015-2518-y Stepanov A. St.Petersburg State University, St.Petersburg State Electrotechnical University, St.Petersburg, Russia aut Non-Abelian K-Theory for Chevalley Groups over Rings [Elektronische Daten] [A. Stepanov] The article contains a survey of the recent author's results on the structure of a Chevalley group G(R) over a ring R. They generalize and improve previously known results on: (1) the relative local-global principle; (2) generators of a relative elementary group; (3) relative multicommutator formulas; (4) the nilpotent structure of a relative K1; (5) the bounded length of commutators. The proof of the first two items is based on computations with generators of the elementary group translated into the language of parabolic subgroups. The other results are proved by means of enlarging a relative elementary group, constructing a generic element, and using the localization procedure in the universal ring. Springer Science+Business Media New York, 2015 Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/4(2015-09-01), 645-656 1072-3374 209:4<645 2015 209 10958 https://doi.org/10.1007/s10958-015-2518-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2518-y text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Stepanov A. St.Petersburg State University, St.Petersburg State Electrotechnical University, St.Petersburg, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 209/4(2015-09-01), 645-656 1072-3374 209:4<645 2015 209 10958