Retraction

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.

Stronger properties

 * Projection on a direct factor

Weaker properties

 * Endomorphism