NCT-subgroup property

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