Results on structure of a Chevalley group $G(R)$ over a ring $R$ obtained recently by the author are anounced. The following results are generalized and improved. (1) Relative local-global principle. (2) Generators of relative elementary subgroups. (3) Relative multi-commutator formulas. (4) Nilpotent structure of relative $\K_1$; (5) Boundedness of commutator length. The proof of first two items is based on computations with generators of the elementary subgroups translated to the language of parabolic subgroups. For the proof of the others we enlarge relative elementary subgroup, construct a generic element, and use localization in a universal ring.
Original languageEnglish
Pages (from-to)645-656
JournalJournal of Mathematical Sciences
Volume209
Issue number4
DOIs
StatePublished - 2015

ID: 5738611