# Function extension expression

This page describes a formal expression, or formalism, that can be used to describe certain subgroup properties.View a complete list of formal expressions for subgroup properties OR View subgroup properties expressible using

thisformalism

## Contents

## Definition

### Main definition

A **function extension expression** is the expression of a subgroup property in terms of two properties of functions (by function here is meant a function from a group to itself). The function extension expression corresponding to function properties and is denoted as:

meaning that satisfies the property in if every function satisfying on , there exists a function satisfying in , and such that .

The property on the left of the arrow is termed the *left side* of the function extension expression, and the property on the right side of the arrow is termed the *right side* of the function extension expression.

## Related formal expressions

## Expressing subgroup properties this way

### Subgroup properties that can be expressed

A subgroup property that can be expressed using a function extension expression is termed a function-extension-expressible subgroup property. A list of all the subgroup properties that are function-extension-expressible is available at Category:Function-extension-expressible subgroup properties.

### Canonical form for expressing a given subgroup property

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