Products of locally cyclic groups

Abstract We consider groups of the form $${G} = {AB}$$ G = AB with two locally cyclic subgroups A and B . The structure these is determined in cases when are both periodic or one them other not. Together a previous study case where torsion-free, this gives complete classification all that product subgroups. As an application, it shown Prüfer rank does not exceed 3, bound sharp. It also proved finite number pairwise permutable supersoluble group. This generalizes well-known theorem B. Huppert for groups.