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Definition

An abelian group$G$ is a divisible group if there exists a multiplicative $\mathbb{Z}_{+}$-action $\alpha:\mathbb{Z}_{+} \to (G \to G)$, where $\mathbb{Z}_{+}$ is the positive integers, such that for all $n:\mathbb{Z}_{+}$ and all $g:G$, the fiber of $\alpha(n)$ at $g$ is contractible: