Locally cyclic torsion-free group
This page describes a group property obtained as a conjunction (AND) of two (or more) more fundamental group properties: locally cyclic group and torsion-free group
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A group is termed a locally cyclic torsion-free group if it satisfies the following equivalent conditions:
- It is both a locally cyclic group (i.e., every finitely generated subgroup is cyclic) and a torsion-free group (i.e., no non-identity element has finite order).
- It is isomorphic to a subgroup of the group of rational numbers.
Equivalence of definitions
Further information: Equivalence of definitions of locally cyclic torsion-free group
Relation with other properties
|Property||Meaning||Proof of implication||Proof of strictness (reverse implication failure)||Intermediate notions|
|Locally cyclic group||every finitely generated subgroup is cyclic|||FULL LIST, MORE INFO|