Galois correspondence-closed 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
This article is about a general term. A list of important particular cases (instances) is available at Category:Galois correspondence-closed subgroup properties

Definition

A Galois correspondence-closed subgroup property is a subgroup property which arises in the following manner.

We start with a rule which, for every group, gives a binary relation between the group and another set constructed canonically from the group. The rule must be isomorphism-invariant, in the sense that any isomorphism of groups respects the binary relation.

The subgroup property we now get is the property of being a subgroup, which is also a closed subset of the group under the Galois correspondence induced by the binary relation.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties