# Function restriction-expressible subgroup property

From Groupprops

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

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

BEWARE!This term is nonstandard and is being used locally within the wiki. [SHOW MORE]

## Definition

### Main definition

A subgroup property is said to be **function restriction-expresssible** if there exist function properties and such that has a restriction formal expression → with respect to the function restriction formalism. In other words, a subgroup satisfies in a group if and only if every function in satisfying property restricts to a function on satisfying property .

## Relation with other metaproperties

### Stronger metaproperties

- Invariance property: This is a subgroup property that can be expressed using the function restriction formalism with the
*right side*being the property of just being a function. - Balanced subgroup property: This is a subgroup property that can be expressed using the function restriction formalism with the left side and the right side being equal.
- Left-inner subgroup property
- Left-extensibility-stable subgroup property