Parabolic subgroups of groups of column-finite infinite matrices

Abstract

For a wide class of rings R that contains all local and semilocal rings, we consider the group SLVK(R) of all matrices over R of the form ab0c, in which a is a finite matrix with determinant 1 and c is an upper triangular infinite matrix with the main diagonal (1,1,…). We describe all subgroups of SLVK(R) that contain all its upper triangular matrices and study their properties.