Group in which every locally finite subgroup is finite
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 properties
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 | |FULL LIST, MORE INFO | |||
| Noetherian group | |FULL LIST, MORE INFO | |||
| group in which every periodic subgroup is finite |