# NCT-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

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Symbol-free definition

A subgroup property is said to be **NCT** if it satisfies all the following conditions:

- It is trivially true
- The only normal subgroup of a group that satisfies it is the trivial subgroup

## Instances

The property of being a core-free subgroup, for instance, is a NCT-subgroup property.

## Relation with other metaproperties

### Opposite metaproperties

An NCT-closed subgroup property cannot be normal closure-closed. Hence, in particular it cannot be join-closed.