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