NCI-subgroup property

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

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.