Periodic subgroup
This article describes a property that arises as the conjunction of a subgroup property: subgroup with a group property (itself viewed as a subgroup property): periodic group
View a complete list of such conjunctions
Definition
A subgroup of a group is termed a periodic subgroup if the subgroup is a periodic group viewed as a group in its own right, i.e., every element of the subgroup has finite order.
Relation with other properties
Stronger properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| finite subgroup | ||||
| subgroup of finite group | ||||
| subgroup of periodic group |
Weaker properties
| Property | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
|---|---|---|---|---|
| local powering-invariant subgroup | periodic implies local powering-invariant | |FULL LIST, MORE INFO | ||
| powering-invariant subgroup | periodic implies powering-invariant | any aperiodic group as a subgroup of itself | |FULL LIST, MORE INFO |