Union-closed group property

Definition
A group property $$p$$ is termed union-closed if whenever a group can be expressed as a union of subgroups, each of which has the property, then the group also has the property. Note that here union is understood to mean set-theoretic union as opposed to join of subgroups.

Weaker metaproperties

 * Finite union-closed group property
 * Join-closed group property
 * Finite join-closed group property