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 …

This note revisits localisation and patching method in the setting of generalised unitary
groups. Introducing certain subgroups of relative elementary unitary groups, we develop …

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 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 …

A new geometric proof is given for the standard description of subgroups in the Chevalley
group $ G= G (\mathrm {F} _4, R) $ of type $\mathrm {F} _4 $ over a commutative ring $ R …

Let Φ be a reduced irreducible root system of rank greater than or equal to 2, let R be a
commutative ring and let I, J be two ideals of R. In the present paper we describe generators …