Definition:Quotient Group

Definition
Let $G$ be a group.

Let $N$ be a normal subgroup of G.

Then the left coset space $G / N$ is a group, where the group product is defined as:
 * $\left({a N}\right) \left({b N}\right) = \left({a b}\right) N$

$G / N$ is called the quotient group (or factor group) of $G$ by $N$.

It is proven to be a group in Quotient Group is a Group.