Infinite groups with rank restrictions on subgroups

Classical results by Mal'cev and Šunkov show that locally nilpotent groups and locally finite groups of infinite rank must contain some abelian subgroups of infinite rank. In recent years, many authors have studied groups in which all subgroups of infinite rank have a given property (which can be either absolute or of embedding type). Results from these researches and some new contributions to this topic are described in this paper.