Fully lattice-determined 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
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VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

A subgroup property p is termed fully lattice-determined if, for any lattice-isomorphic groups G_1, G_2, any lattice isomorphism \varphi: L(G_1) \to L(G_2), and any subgroup H_1 of G_1, H_1 satisfies p in G_1 if and only if \varphi(H_1) satisfies p in G_2.

Relation with other metaproperties

Weaker metaproperties

Metaproperty Meaning Proof of implication Proof of strictness (reverse implication failure) Intermediate notions
conditionally lattice-determined subgroup property determined up to lattice automorphisms (i.e., holding the ambient group constant) |FULL LIST, MORE INFO