Join-closed group property

Definition
A group property $$p$$ is termed join-closed if given a nonempty collection of subgroups, each of which has the property $$p$$ as an abstract group, so does their join i.e. the subgroup generated by them.

Weaker metaproperties

 * Stronger than::Union-closed group property
 * Stronger than::Normal join-closed group property
 * Stronger than::Finite join-closed group property
 * Stronger than::ACU-closed group property