Union-closed group property
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
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A group property is termed union-closed if whenever a group can be expressed as a union of subgroups, each of which has the property, then the group also has the property. Note that here union is understood to mean set-theoretic union as opposed to join of subgroups.