The additive group Z of integers is generator by 1 but additive group of rational numbers is not why?
2026-03-26 16:06:16.1774541176
The additive group of rationals is not finitely generated
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For a finite number of rationals $q_1,\ldots,q_n \in \mathbb{Q}$, consider the group generated by these rationals. What can you say about the denominator of any number (when written in reduced form) in this group?