Strongly intersection-closed subgroup property
This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property
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A subgroup property is said to be strongly intersection-closed if given any arbitrary (possibly empty) family of subgroups each satisfying the subgroup property in the group, the intersection of all the subgroups again satisfies the property.
Definition with symbols
A subgroup property is termed strongly intersection-closed if given any group and any (possibly empty) family of subgroups of indexed by such that each satisfies in , the group also satisfies in .
Relation with other metaproperties
- Strongly UL-intersection-closed subgroup property
- Invariance property: For full proof, refer: Invariance implies strongly intersection-closed