divisible group
An abelian group^{} $D$ is said to be divisible if for any $x\in D$, $n\in {\mathbb{Z}}^{+}$, there exists an element ${x}^{\prime}\in D$ such that $n{x}^{\prime}=x$.
Some noteworthy facts:

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An abelian group is injective^{} (http://planetmath.org/InjectiveModule) (as a $\mathbb{Z}$module) if and only if it is divisible.

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Every group is isomorphic^{} to a subgroup^{} of a divisible group.

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Any divisible abelian group is isomorphic to the direct sum^{} of its torsion subgroup and $n$ copies of the group of rationals (for some cardinal number^{} $n$).
Title  divisible group 

Canonical name  DivisibleGroup 
Date of creation  20130322 13:47:17 
Last modified on  20130322 13:47:17 
Owner  mathcam (2727) 
Last modified by  mathcam (2727) 
Numerical id  7 
Author  mathcam (2727) 
Entry type  Definition 
Classification  msc 20K99 