Subgroup-closed group property

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This article defines a group metaproperty: a property that can be evaluated to true/false for any group property
View a complete list of group metaproperties


Symbol-free definition

A group property is said to be subgroup-closed or S-closed if any subgroup of a group having the property also has the property.

Definition with symbols

A group property p is said to be subgroup-closed or S-closed if whenever G satisfies property p and H is a subgroup of G, H must also satisfy property p.

Relation with other metaproperties

Stronger metaproperties

Weaker metaproperties