Locally free 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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This is a variation of free group|Find other variations of free group |

Definition

A group is termed a locally free group if every finitely generated subgroup of it is a free group.

Formalisms

In terms of the locally operator

This property is obtained by applying the locally operator to the property: free group
View other properties obtained by applying the locally operator

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
locally cyclic aperiodic group	locally free and abelian; equivalently, locally cyclic and aperiodic	(by definition)		|FULL LIST, MORE INFO
free group	free on some generating set	freeness is subgroup-closed	locally free not implies free	|FULL LIST, MORE INFO
countably free group	every countable subgroup is free	follows from finitely generated implies countable	The group of rational numbers is locally free but not countably free	|FULL LIST, MORE INFO

Weaker properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
locally residually finite group