  The classical result, due to Jordan, Burnside, Dickson, says that every
normal subgroup of $GL(n, K)$ ($K$ - a field, $n \geq 3$) which is not
contained in the center, contains $SL(n, K)$. A. Rosenberg gave description of
normal subgroups of $GL(V)$, where $V$ 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 $g$ such that $g-id_V$ has finite dimensional range the proof
is not complete. We fill this gap for countably dimensional $V$ giving
description of the lattice of normal subgroups in the group of infinite
column-finite matrices indexed by positive integers over any field.
