# Subgroup in which every relatively normal subgroup is weakly closed

From Groupprops

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