Lattice-determined group property

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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 isomorphic lattices of subgroups, either both G_1 and G_2 have p, or neither does.