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.