# Group in which every periodic subgroup is locally 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 periodic subgroup is locally finite** is a group satisfying the following equivalent conditions:

- Every perodic subgroup of the group is locally finite
- Every finitely generated periodic subgroup of the group is finite

## Relation with other properties

### Stronger properties

Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|

group in which every periodic subgroup is finite | ||||

abelian group | follows from equivalence of definitions of periodic abelian group | |||

nilpotent group | follows from equivalence of definitions of periodic nilpotent group |