Free abelian group of rank three

Definition
The free abelian group of rank three is defined as the free abelian group of rank three. Explicitly, it is defined as the external direct product of three copies of the group of integers, and is denoted $$\mathbb{Z} \times \mathbb{Z} \times \mathbb{Z}$$ or $$\mathbb{Z}^3$$.

It can also be defined as the abelianization of the free group of rank three.