Abelian-tautological 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 $p$ is termed abelian-tautological if given any abelian group $G$ and any subgroup $H$ of $G$ (so $H$ is a subgroup of abelian group), $H$ satisfies $p$ in $G$.