# Function property

From Groupprops

This article is about a general term. A list of important particular cases (instances) is available at Category:Function properties

## Contents |

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## Definition

A **function property** is a map from the collection of all possible functions from a group to itself, to the two-element set (true, false). A function which gets mapped to *true* is said to *have* the function property, and a function which gets mapped to *false* is said to *not have* the function property.

The function property must satisfy *isomorphism-invariance*: if and are functions, and there is an isomorphism such that , then satisfies the function property iff satisfies the function property.