Group in which every periodic 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
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Definition
A group in which every periodic subgroup is finite is a group in which every periodic subgroup (i.e., every subgroup that is a periodic group) is a finite subgroup (i.e., it is a finite group).
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| finite group | ||||
| aperiodic group |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| group in which every locally finite subgroup is finite |