Integers Modulo m under Addition form Abelian Group

Theorem
Let $\Z_m$ is the set of integers modulo $m$

Let $+_m$ be the operation of addition modulo $m$.

Then the structure $\struct {\Z_m, +_m}$ is an abelian group.

Proof
From Integers Modulo m under Addition form Cyclic Group, $\struct {\Z_m, +_m}$ is a cyclic group.

The result follows from Cyclic Group is Abelian.