Finite-upper join-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 a finite-upper join-closed subgroup property if, for any subgroup H of a group G, and any intermediate subgroups K_1, K_2 of G such that H satisfies p in both K_1 and K_2, we have that H satisfies p in the join of subgroups \langle K_1, K_2 \rangle.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties