# Strongly UL-intersection-closed subgroup property

From Groupprops

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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 metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Definition

A subgroup property is termed **strongly UL-intersection-closed** if for any group , any (possibly empty) indexing set , and subgroups , such that satisfies property in for each , we have:

satisfies property in .

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