Finite-upper join-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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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

• Upper join-closed subgroup property

Weaker metaproperties

• Permuting upper join-closed subgroup property