# Retraction

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

## Definition

### Symbol-free definition

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

### Definition with symbols

A retraction of a group $G$ is an endomorphism $f:G \to G$ such that $f^2 = f$, in other words, $f(f(g)) = f(g)$ for every $g \in G$. The image of $f$ is termed a retract, and the retraction can also be viewed as a map from $G$ to the subgroup which is this image.