# NCI-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 a **NCI-subgroup property** if it satisfies the following conditions:

- It is identity-true
- The only normal subgroup of a group which satisfies the property is the whole group

## Instances

## Relation with other metaproperties

### Opposite metaproperties

Any NCI-subgroup property that is not itself the property of being the whole group (that is, it is satisfied by at least one proper subgroup) cannot be normal core-closed. Hence, it also cannot be intersection-closed.