Conditionally lattice-determined subgroup property
From Groupprops
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
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions
Definition
A subgroup property is termed conditionally lattice-determined if, for any group
, any lattice automorphism
of the lattice of subgroups
, and any subgroup
of
,
satisfies
if and only if
satisfies
.
The use of the qualifier conditionally is to contract with fully lattice-determined subgroup property, where we allow the ambient group to also vary.
Relation with other metaproperties
Stronger metaproperties
Metaproperty | Meaning | Proof of implication | Proof of strictness (reverse implication failure) | Intermediate notions |
---|---|---|---|---|
fully lattice-determined subgroup property | determined up to lattice isomorphism (between possibly non-isomorphic ambient groups) | |FULL LIST, MORE INFO |