In the current article we study the structure of a Chevalley group G (R) over a commutative
ring R. We generalize and improve the following results on:• the standard, relative, and multi …

Let $ G $ be a not necessarily split reductive group scheme over a commutative ring $ R $
with $1 $. Given a parabolic subgroup $ P $ of $ G $, the elementary group $\mathrm {E} _P …

This paper studies the work of Bak in algebra and (lower) algebraic K-theory and some later
developments stimulated by them. We present an overview of his work in these areas …

The present paper is the [slightly expanded] text of our talk at the Conference" Advances in
Group Theory and Applications" at Porto Cesareo in June 2011. Our main results assert that …

Let G be a reductive algebraic group over a field k, such that every semisimple normal
subgroup of G has isotropic rank≥ 2, ie contains (Gm) 2. Let K1G be the non-stable K1 …

Abstract Let G= G (Φ, R) be the simply connected Chevalley group with root system Φ over a
ring R. Denote by E (Φ, R) its elementary subgroup. The main result of the article asserts that …

Let G and E stand for one of the following pairs of groups:• Either G is the general quadratic
group U (2n, R, Λ), n≥ 3, and E its elementary subgroup EU (2n, R, Λ), for an almost …

We describe a connection between the combinatorics of generators for certain groups and
the combinatorics of Helly's 1913 theorem on convex sets. We use this connection to prove …

In the present paper, we discuss some recent versions of localization methods for
calculations in the groups of points of algebraic-like and classical-like groups. Namely, we …

In this paper we consider Chevalley groups over commutative rings with $1 $, constructed
by irreducible root systems of rank $> 1$. We always suppose that for the systems $ A_2 …