Strongly UL-intersection-closed subgroup property

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This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
View a complete list of subgroup metaproperties
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

A subgroup property p is termed strongly UL-intersection-closed if for any group G, any (possibly empty) indexing set I, and subgroups H_i \le K_i \le G, i \in I, such that H_i satisfies property p in K_i for each i \in I, we have:

\bigcap_{i \in I} H_i satisfies property p in \bigcap_{i \in I} K_i.

A subgroup property is strongly UL-intersection-closed if and only if it is both UL-intersection-closed and identity-true.

Relation with other metaproperties

Weaker metaproperties