# Hall-relatively weakly closed subgroup

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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

Suppose is a finite group and is a subgroup of . We say that is a **Hall-relatively weakly closed subgroup** of if, for any group containing as a Hall subgroup, is a weakly closed subgroup of relative to .

## Relation with other properties

### Stronger properties

- Isomorph-free subgroup
- Sylow-relatively weakly closed subgroup: The same definition, but restricted to the case where is a group of prime power order.