Locally cyclic group
This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
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A group is termed locally cyclic if it satisfies the following equivalent conditions:
- Every finitely generated subgroup of the group is cyclic.
- The subgroup generated by any two elements of the group is cyclic.
- Its lattice of subgroups is a distributive lattice. In other words, the operations of join of subgroups and intersection of subgroups distribute over each other.