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 operation is defined as:
 * $\paren {a N} \paren {b N} = \paren {a b} N$

$G / N$ is called the quotient group of $G$ by $N$.

Also see

 * Quotient Group is Group, where $G / N$ is proven to be a group


 * From Subgroup is Normal iff Left Cosets are Right Cosets, the left coset space is equal to the right coset space.

It follows that $G / N$ does not depend on whether left cosets are used to define it or right cosets.

Thus we do not need to distinguish between the left quotient group and the right quotient group - the two are one and the same.


 * Definition:Quotient Group Epimorphism