# Periodic normal subgroup

From Groupprops

This article describes a property that arises as the conjunction of a subgroup property: normal subgroup with a group property (itself viewed as a subgroup property): periodic group

View a complete list of such conjunctions

## Contents

## Statement

A subgroup of a group is termed a **periodic normal subgroup** if it satisfies the following two conditions:

- It is a normal subgroup of the whole group.
- It is a periodic group: every element has finite order.

## Relation with other properties

### Stronger properties

### Weaker properties

- Amalgam-characteristic subgroup:
*For proof of the implication, refer Periodic normal implies amalgam-characteristic and for proof of its strictness (i.e. the reverse implication being false) refer Amalgam-characteristic not implies periodic normal*. - Potentially characteristic subgroup
- Normal subgroup

## Metaproperties

### Quotient-transitivity

This subgroup property is quotient-transitive: the corresponding quotient property is transitive.

View a complete list of quotient-transitive subgroup properties