Editing Locally cyclic group (section)

==Some facts==
* Every cyclic group is locally cyclic, and every locally cyclic group is [[abelian group|abelian]].{{sfnp|Rose|2012|p=54}}
* Every finitely-generated locally cyclic group is cyclic.
* Every [[subgroup]] and [[quotient group]] of a locally cyclic group is locally cyclic.
* Every [[group homomorphism|homomorphic]] image of a locally cyclic group is locally cyclic.
* A group is locally cyclic if and only if every pair of elements in the group generates a cyclic group.
* A group is locally cyclic if and only if its [[lattice of subgroups]] is [[distributive lattice|distributive]] {{harv|Ore|1938}}.
* The [[torsion-free rank]] of a locally cyclic group is 0 or 1.
* The [[endomorphism ring]] of a locally cyclic group is [[commutative ring|commutative]].{{citation needed|date=June 2015}}