In-normalizer 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

A subgroup property in a group is said to be an in-normalizer subgroup property if the following is true: a subgroup satisfies the property in the whole group if and only if it satisfies the property in its normalizer. Equivalently, a subgroup property is an in-normalizer subgroup property if it is fixed under the idempotent in-normalizer operator on subgroup properties.