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 $b N$ be defined as:


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

Alternatively, the product of the cosets $a N$ and $b N$ can be defined as:


 * $\left({a N}\right) \left({b N}\right) = \left\{{x y: x \in a N, y \in b N}\right\}$

that is, using the definition from subset product.

Also see

 * Coset Product is Well-Defined