LAUSR

Abstract The classical result, due to Jordan, Burnside, Dickson, says that every normal subgroup of GL⁢(n,K)\mathrm{GL}(n,K), where ???? is a field and n≥3n\geq 3, which is not contained in the center contains SL⁢(n,K)\mathrm{SL}(n,K). Rosenberg described the normal subgroups of GL⁢(V)\mathrm{GL}(V), where ???? is a vector space of any infinite cardinality dimension over a division ring. However, when he considers subgroups of the direct product of the center and the group of linear transformations ???? such that g-idVg-\mathrm{id}_{V} has finite-dimensional range, the proof is incomplete. We fill this gap for countably dimensional ???? giving description of the lattice of normal subgroups in the group of infinite column-finite matrices indexed by positive integers over any field.