NCI-subgroup property

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 metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

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

• Contranormal subgroup
• Self-normalizing subgroup
• Abnormal subgroup

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.