\begin{definition}[Definition:Quotient Epimorphism/Group]
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 $q_N: G \to G / N$ defined as:
:$\forall x \in G: \map {q_N} x = x N$
is known as the '''quotient (group) epimorphism''' from $G$ to $G / N$.
\end{definition}