The subnormal subgroup structure of the infinite general linear group

Abstract

Let R be a ring with identity, let Ω be an infinite set and let M be the free R-module R(Ω). In [1] we investigated the problem of locating and classifying the normal subgroups of GL(Ω, R), the group of units of the endomorphism ring EndRM, where R was an arbitrary ring with identity. (This extended the work of [3] and [8] where it was necessary for R to satisfy certain finiteness conditions.) When R is a division ring, the complete classification of the normal subgroups of GL(Ω, R) is given in [9] and the corresponding results for a Hilbert space are given in [6] and [7]. The object of this paper is to extend the methods of [1] to yield a classification of the subnormal subgroups of GL(Ω, R) along the lines of that given by Wilson in [10] in the finite dimensional case.