Group in which every locally finite subgroup is finite

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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

Definition

A group in which every locally finite subgroup is finite is a group in which every subgroup that is locally finite as a group must be a finite subgroup, i.e., it is finite as a group.

Relation with other properties

Stronger properties

Property Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
aperiodic group
finite group Group in which every periodic subgroup is finite, Noetherian group|FULL LIST, MORE INFO
Noetherian group |FULL LIST, MORE INFO
group in which every periodic subgroup is finite