Normalizer-closed 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

Statement

A subgroup property $p$ is termed normalizer-closed if the normalizer of any subgroup satisfying property $p$ also satisfies property $p$.

Relation with other properties

Stronger properties

• Upward-closed subgroup property
• Auto-invariance property
• Automorphism-based relation-implication-expressible subgroup property