# 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 Intermediately local powering-invariant subgroup|FULL LIST, MORE INFO
powering-invariant subgroup periodic implies powering-invariant any aperiodic group as a subgroup of itself Intermediately local powering-invariant subgroup, Intermediately powering-invariant subgroup, Local powering-invariant subgroup|FULL LIST, MORE INFO