Lattice-determined group property

This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
View a complete list of group metaproperties

Definition

A group property $p$ is termed lattice-determined if it can be expressed as a condition on the lattice of subgroups. Explicitly, this means that given two groups $G_1, G_2$ that are lattice-isomorphic groups, i.e., they have isomorphic lattices of subgroups, either both $G_1$ and $G_2$ have $p$, or neither does.