Definition:Quotient Epimorphism/Group

Definition
Let $G$ be a group.

Let $N$ be a normal subgroup of $G$.

Let $G / N$ be the quotient group of $G$ by $N$.

The mapping $q: G \to G / N$ defined as:
 * $q: G \to G / N: q \left({x}\right) = x N$

is known as the natural epimorphism from $G$ to $G / N$.

Also known as
The natural epimorphism is also known as:
 * the natural morphism
 * the natural homomorphism
 * the quotient epimorphism
 * the quotient morphism
 * the canonical epimorphism
 * the canonical morphism.

Also see

 * Natural Epimorphism is Epimorphism