Retraction

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Template:Endomorphism property

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.

Relation with other properties

Stronger properties

Weaker properties