Definition:Coset Product

Definition
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 the map:


 * $\circ : G/N \times G/N \to G/N$

such that:


 * $\paren {a \circ N} \circ \paren {b \circ N} = \paren {a \circ b} \circ N$

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

Also see

 * Coset Product is Well-Defined
 * Coset Product of Normal Subgroup is Consistent with Subset Product Definition