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

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## Definition

This group can be defined in the following equivalent ways:

- It is the external direct product of the group of rational numbers and the group of rational numbers modulo integers . Explicitly, it is the group .
- 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 .