Izable 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
View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metaproperty
VIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

Definition

Definition with symbols

A subgroup property p is termed izable if for any subgroup H of a group G, there is a unique subgroup M of G such that all these conditions are satisfied:

  • M contains H
  • Let L be a subgroup of G containing H. Then H satisfies p in L if and only if L is contained in M.

Equivalently, a subgroup property is izable if it is upper join-closed, identity-true and satisfies the intermediate subgroup condition.

Relation with other metaproperties

Weaker metaproperties