# Difference between revisions of "Locally cyclic group"

A group in which every finitely generated subgroup is cyclic. In such a group, either every element is of finite order (periodic), or no element other than the identity is (aperiodic). The additive group of rational numbers $\mathbb{Q}^+$ is an aperiodic example, and the group $\mathbb{Q}/\mathbb{Z}$ is a periodic example. The lattice of subgroups of a group is a distributive lattice if and only if the group is locally cyclic.