Normalizer-closed subgroup property

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

Stronger properties

 * Weaker than::Upward-closed subgroup property
 * Weaker than::Auto-invariance property
 * Weaker than::Automorphism-based relation-implication-expressible subgroup property