Directed union-closed group property
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This article defines a group property: a property that can be evaluated to true/false for any given group, invariant under isomorphism
View a complete list of group properties
VIEW RELATED: Group property implications | Group property non-implications |Group metaproperty satisfactions | Group metaproperty dissatisfactions | Group property satisfactions | Group property dissatisfactions
A group property is termed directed union-closed if given any directed set of subgroups of the group, each satisfying the property, their union also satisfies the property.
Definition with symbols
A group property is termed directed union-closed if given any group , any nonempty directed set , and a collection of subgroups of such that , such that each satisfies , the union:
also satisfies .
Relation with other metaproperties
- Join-closed group property
- Union-closed group property
- Varietal group property: For full proof, refer: Varietal implies directed union-closed