Integer_Multiples_under_Addition_form_Infinite_Cyclic_Group

Let $n \Z$ be the set of integer multiples of $n$. Then $\struct {n \Z, +}$ is a countably infinite cyclic group. It is generated by $n$ and $-n$ $n \Z = \gen n$ $n \Z = \gen {-n}$ Hence $\struct {n \Z, +}$ can be justifiably referred to as the additive group of integer multiples.