Locally free group

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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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VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
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 Countably free group|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