# Retraction

From Groupprops

Template:Endomorphism property

*This article defines a notion of an idempotent (one that equals its square) in a certain context*

## Contents

## Definition

### Symbol-free definition

A retraction is an idempotent endomorphism from a group to itself.

### Definition with symbols

A **retraction** of a group is an endomorphism such that , in other words, for every . The image of is termed a retract, and the retraction can also be viewed as a map from to the subgroup which is this image.