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 …

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 …

We revisit localisation and patching method in the setting of Chevalley groups. Introducing
certain subgroups of relative elementary Chevalley groups, we develop relative versions of …

Let A be a quasi-finite R-algebra (ie, a direct limit of module finite algebras) with identity. Let
I i, i= 0,…, m, be two-sided ideals of A, GL n (A, I i) be the principal congruence subgroup of …

In his seminal paper, half a century ago, Hyman Bass established commutator formulas for a
(stable) general linear group, which were the key step in defining the group K 1. Namely, he …

In the present paper, which is a direct sequel of our paper [14] joint with Roozbeh Hazrat, we
prove an unrelativized version of the standard commutator formula in the setting of …

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 …

In the present note, which is a marginalia to the previous papers by Roozbeh Hazrat, Alexei
Stepanov, Zuhong Zhang, and the author, I observe that for any ideals A, B⊴ R of a …

In the present paper, we describe some recent applications of localization methods to the
study of commutators in the groups of points of algebraic and algebraic-like groups, such as …

Suslin's local-global principle asserts that if a matrix over a polynomial ring vanishes modulo
the independent variable and is locally elementary then it is elementary. In this article we …