# Fusion system-relatively weakly closed subgroup

From Groupprops

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The article defines a subgroup property, where the definition may be in terms of a particular prime number that serves as parameter

View other prime-parametrized subgroup properties | View all subgroup properties

## Definition

Suppose is a group of prime power order, i.e., a finite -group for some prime number . A subgroup of is termed a **fusion system-relatively weakly closed subgroup** if is a weakly closed subgroup for any fusion system on .

## Relation with other properties

### Stronger properties

- Isomorph-normal coprime automorphism-invariant subgroup of group of prime power order:
`For full proof, refer: Isomorph-normal coprime automorphism-invariant implies weakly closed for any fusion system` - Fusion system-relatively strongly closed subgroup