Directed union-closed group property

Symbol-free definition
A group property is termed directed union-closed if given any directed set of subgroups of the group, each satisfying the property, their union also satisfies the property.

Definition with symbols
A group property $$p$$ is termed directed union-closed if given any group $$G$$, any nonempty directed set $$I$$, and a collection of subgroups $$H_i, i \in I$$ of $$G$$ such that $$i < j \implies H_i \le H_j$$, such that each $$H_i$$ satisfies $$p$$, the union:

$$\bigcup_{i \in I} H_i$$

also satisfies $$p$$.

Stronger metaproperties

 * Weaker than::Join-closed group property
 * Weaker than::Union-closed group property
 * Weaker than::Varietal group property:

Weaker metaproperties

 * Stronger than::ACU-closed group property