Quotient Structure of Abelian Group is Abelian Group

Theorem
Let $\RR$ be a congruence relation on an abelian group $\struct {G, \circ}$.

Then the quotient structure $\struct {G / \RR, \circ_\RR}$ is an abelian group.

Proof
From Quotient Structure of Group is Group we have that $\struct {G / \RR, \circ_\RR}$ is a group.

Let $\eqclass x \RR, \eqclass y \RR \in S / \RR$.

Hence $\circ_{S / \RR}$ is commutative.

Hence $\struct {G / \RR, \circ_\RR}$ is an abelian group.