ACU-closed group property

Symbol-free definition
A group property is termed ACU-closed if, whenever there is an ascending chain of subgroups in a group, each having the group property, the union of those subgroups also has the property.

Definition with symbols
A group property $$p$$ is termed ACU-closed if, for any group $$G$$, any nonempty totally ordered set $$I$$, and any ascending chain $$H_i$$ of subgroups of $$G$$ indexed by ordinals $$i \in I$$ such that $$H_i \le H_j$$ for $$i < j$$, the subgroup:

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

also satisfies property $$p$$.

Stronger metaproperties

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