# Balanced subgroup property (generic notion)

*This article is about the general notion of balanced subgroup property. For the typical use of balanced subgroup property in the context of the function restriction formalism, refer balanced subgroup property (function restriction formalism)*.

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

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

## Definition

### Symbol-free definition

We need to have two inputs with respect to which we can talk of balanced subgroup property:

- A relational mapping system
- A specification of one of these formalisms based on the relational mapping system: the restriction formalism, the extension formalism, the [[[universal restriction formalism]], the universal extension formalism, the when-defined restriction formalism, the when-defined extension formalism

For a given formalism based on the relational mapping system, a subgroup property is termed **balanced** if it has a formal expression (in that formalism) with equal left and right sides.

### Definition with symbols

We need to have two inputs with respect to which we can talk of balanced subgroup property:

- A relational mapping system
- A specification of one of these formalisms based on the relational mapping system: the restriction formalism, the extension formalism, the [[[universal restriction formalism]], the universal extension formalism, the when-defined restriction formalism, the when-defined extension formalism

For a given formalism based on the relational mapping system, a subgroup property is termed **balanced** if it has a formal expression (in that formalism) of the form → .