# Group in which every locally finite subgroup is finite

From Groupprops

This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism

View a complete list of group propertiesVIEW 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 |