# WNSCC-subgroup

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 of a group is termed a **WNSCC-subgroup**, or a **weak normal subset-conjugacy-closed subgroup**, if it is weak normal subset-conjugacy-determined in itself, relative to the whole group.

### Definition with symbols

A subgroup of a group is termed a **WNSCC-subgroup** or **weak normal subset-conjugacy-closed subgroup** in if it satisfies the following condition: For any two normal subsets of such that there exists with , we have .

## Relation with other properties

### Stronger properties

- Abnormal subgroup:
`For full proof, refer: Abnormal implies WNSCC` - Direct factor
- Central factor
- Retract
- Subset-conjugacy-closed subgroup
- Normal subset-conjugacy-closed subgroup