On arrangement of subgroups in groups and related topics: some recent developments

Investigation of groups satisfying certain conditions, related to the subgroup arrangement, enabled algebraists to introduce and describe many important classes of groups. The roots of such investigations lie in the works by P. Hall, R. Carter, J. Rose, and Z. Borevich. Numerous interesting results in this area have been obtained lately by many authors. The main goal of this survey is to reflect some important new developments in study of subgroup arrangement in infinite groups.