Products of locally cyclic groups

We consider groups of the form $G=AB$ with two locally cyclic subgroups $A$ and $B$. The structure of these groups is determined in the cases when $A$ and $B$ are both periodic or when one of them is periodic and the other is not. Together with a previous study of the case when $A$ and $B$ are torsion-free, this gives a complete classification of all groups that are the product of two locally cyclic groups. It is also shown that the product of a finite number of pairwise permutable periodic locally cyclic subgroups is a locally supersoluble group.