The Additive Group of Rational Numbers and The Multiplicative Group of Positive Rational Numbers are Not Isomorphic
Problem 510
Let $(\Q, +)$ be the additive group of rational numbers and let $(\Q_{ > 0}, \times)$ be the multiplicative group of positive rational numbers.
Prove that $(\Q, +)$ and $(\Q_{ > 0}, \times)$ are not isomorphic as groups.
