Finite-relative-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 finite-relative-intersection-closed if it satisfies the following:

Suppose H,K are subgroups of a group G such that H satisfies property p in G and K satisfies property p in some subgroup of G containing both H and K. Then, H \cap K satisfies property p in G.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties

Facts