On groups in which every subgroup of infinite rank is subnormal of bounded defect

A special case of the main result is as follows: Let G be a locally (soluble-by-finite) group of infinite rank in which every subgroup of infinite rank is subnormal of defect at most d. Then G is nilpotent of class bounded in terms of d only. This extends a famous theorem of Roseblade and holds, more generally, for groups G that belong to the class ks introduced by Cernikov. It is also shown that G is a Dedekind group if d = 1.