Locally cyclic group

In group theory, a **locally cyclic group** is a type of group that is, in a certain sense, generated by its own elements in a cyclic manner. More formally, a group \( G \) is said to be locally cyclic if every finitely generated subgroup of \( G \) is cyclic. This means that for any finite set of elements from \( G \), the subgroup generated by those elements can be generated by a single element.