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A [[group]] is termed '''locally cyclic''' if it satisfies the following equivalent conditions:
# Every [[finitely generated group|finitely generated]] subgroup of the group is [[cyclic group|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.
==Relation with other properties==