# Normal join-closed group property

From Groupprops

This article defines a group metaproperty: a property that can be evaluated to true/false for any group property

View a complete list of group metaproperties

## Contents

## Definition

### Symbol-free definition

A group property is said to be **normal join-closed** or **N-closed** if it satisfies the following. Whenever there are two normal subgroups of a group, both having the property as abstract groups, then their join also has the property as an abstract group.

### Definition with symbols

A group property is said to be **normal join-closed** or **N-closed** if whenever such that and both satisfy as abstract groups, so does .