Is there a natural example of a divisible torsioned (= periodic) abelian group?

The simplest example is the quotient $\mathbb{Q}/\mathbb{Z}$, i.e. the additive rational numbers modulo $1$. This is divisible for the same reason that $\mathbb{Q}$ is, and is torsion since any rational number has an integer multiple.

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Logic

Abstract Algebra

Group Theory

Model Theory

Abelian Groups

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