Subgroup in which every relatively normal subgroup is weakly closed

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This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

Definition

Symbol-free definition

A subgroup in which every relatively normal subgroup is weakly closed is a subgroup in which every relatively normal subgroup (i.e., every subgroup that is normal inside the subgroup) is weakly closed.

Definition with symbols

A subgroup K of a group G is termed a subgroup in which every relatively normal subgroup is weakly closed if, for any subgroup H of K that is a normal subgroup of K (not necessarily of G, H is a weakly closed subgroup in K with respect to G.

Relation with other properties

Stronger properties