\begin{definition}[Definition:Coset Product]
Let $\struct {G, \circ}$ be a group.
Let $N$ be a normal subgroup of $G$.
Let $a, b \in G$.
The '''coset product''' of $a \circ N$ and $b \circ N$ is defined as:
:$\paren {a \circ N} \circ \paren {b \circ  N} = \paren {a \circ b} \circ N$
where $a \circ N$ and $b \circ N$ are the left cosets of $a$ and $b$ by $N$.
\end{definition}