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An abelian group GG is a divisible group if there exists a leftℤ +\mathbb{Z}_{+}-action (α−)(−):ℤ + × →(G→G) (-)(-):\mathbb{Z}_{+} \alpha:\mathbb{Z}_{+} \times G \to G (G \to G), where ℤ +\mathbb{Z}_{+} is the positve positive integers, such that for alln:ℤ +n:\mathbb{Z}_{+} and all g:Gg:G, the fiber of n α(−n) n(-) \alpha(n) at gg is contractible:
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