Direct product of group of rational numbers and group of rational numbers modulo integers

Definition
This group can be defined in the following equivalent ways:


 * 1) It is the external direct product of the group of rational numbers $$\mathbb{Q}$$ and the group of rational numbers modulo integers $$\mathbb{Q}/\mathbb{Z}$$. Explicitly, it is the group $$\mathbb{Q} \times \mathbb{Q}/\mathbb{Z}$$.
 * 2) It is the external central product of two copies of the group of rational numbers where we identify a copy of the group of integers in group of rational numbers in both groups with each other. Explicitly, it is the central product of $$\mathbb{Q} *_\mathbb{Z} \mathbb{Z}$$.

Related groups

 * Amalgamated free product of two copies of group of rational numbers over group of integers