Normal join-closed group property

Symbol-free definition
A group property $$p$$ is said to be normal join-closed or N-closed if it satisfies the following. Whenever there are two normal subgroups of a group, both having the property as abstract groups, then their join also has the property as an abstract group.

Definition with symbols
A group property $$p$$ is said to be normal join-closed or N-closed if whenever $$N_1, N_2 \triangleleft G$$ such that $$N_1$$ and $$N_2$$ both satisfy $$p$$ as abstract groups, so does $$N_1N_2$$.

Stronger metaproperties

 * Join-closed group property

Weaker metaproperties

 * Direct product-closed group property
 * Central product-closed group property