# Normal 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 **normal core-closed** if whenever a subgroup has the property in the whole group, its normal core also has the property.

### Definition with symbols

A subgroup property is said to be **normal core-closed** if whenever satisfies property in , the normal core also satisfies in .

## Relation with other metaproperties

### Stronger metaproperties

- Intersection-closed subgroup property
- Finite-intersection-closed subgroup property when we are guaranteed that there are only finitely many conjugates
- Conjugate-intersection-closed subgroup property