Definition:Coset Product

Definition
Let $\left({G, \circ}\right)$ be a group.

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

Let $a, b \in G$.

The coset product of $a N$ and $b N$ is defined as:


 * $\left({a \circ N}\right) \circ \left({b \circ N}\right) = \left({a \circ b}\right) \circ N$

where $a \circ N$ and $b \circ N$ are the left cosets of $a$ and $b$ by $N$.

Also see

 * Coset Product is Well-Defined


 * Coset Product of Normal Subgroup is Consistent with Subset Product Definition