Open main menu

Groupprops β

Function property

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


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

Contents

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 f_1:G \to G and f_2:H \to H are functions, and there is an isomorphism \sigma:G \to H such that \sigma \circ f_1 = f_2 \circ \sigma, then f_1 satisfies the function property iff f_2 satisfies the function property.