Normal subgroups of the group of column-finite infinite matrices

Waldemar Hołubowski, Martyna Maciaszczyk, Sebastian Żurek

Published 2018-08-21Version 1

The classical result due to Jordan, Burnside, Dickson, says that every normal subgroup of GL(n;K) (K - a field, n >= 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. However, in countable case his result is incomplete. We fill this gap giving description of the lattice of normal subgroups of the group of infinite column-finite matrices indexed by positive integers over any field.