I'm looking for an example of a group operation on the rationals, which is not isomorphic to the rational additive group. Can you find such an example?
2026-04-07 02:51:32.1775530292
An example of a group operation on the rationals, which is not isomorphic to the additive group
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$\mathbb{F}_2[x]$ as an additive group is countable. It has a number of elements of order $2$, which shows it is not isomorphic to $\mathbb{Q}^+$. Construct a bijection between these sets and you're good.