# Characteristic core-closed subgroup property

From Groupprops

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

View a complete list of subgroup metaproperties

View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Contents

## Definition

### Symbol-free definition

A subgroup property is said to be **characteristic core-closed** if whenever a subgroup has the proeprty in the whole group, so does its characteristic core (viz the largest characteristic subgroup contained inside it).

### Definition with symbols

A subgroup property is said to be **characteristic core-closed** if whenever satisfies property in , and is the characteristic core of , satisfies property in .