Fully lattice-determined subgroup property

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