Definition:Additive Group of Integers Modulo m

Definition
Let $m \in \Z$ such that $m > 1$.

The additive group of integers modulo $m$ $\left({\Z_m, +_m}\right)$ is the set of integers modulo $m$ under the operation of addition modulo $m$.

Cayley Table for Additive Group of Integers Modulo 4
The additive group of integers modulo $4$ can be described by showing its Cayley table:

Also see

 * Integers Modulo m under Addition form Cyclic Group