# Finite-relative-intersection-closed subgroup property

From Groupprops

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This article defines a subgroup metaproperty: a property that can be evaluated to true/false for any subgroup property

View a complete list of subgroup metaproperties

View subgroup properties satisfying this metaproperty| View subgroup properties dissatisfying this metapropertyVIEW RELATED: subgroup metaproperty satisfactions| subgroup metaproperty dissatisfactions

## Definition

A subgroup property is termed **finite-relative-intersection-closed** if it satisfies the following:

Suppose are subgroups of a group such that satisfies property in and satisfies property in some subgroup of containing both and . Then, satisfies property in .

## Relation with other metaproperties

### Stronger metaproperties

### Weaker metaproperties

## Facts

- A transitive subgroup property that also satisfies the transfer condition is finite-relative-intersection-closed.
`For full proof, refer: Transitive and transfer condition implies finite-relative-intersection-closed`