divisible closure

Let $G$ be a torsion-free abelian group. We will say that $D$ is the divisible closure of $G$ if $D$ is the only divisible torsion-free group between $G$ and $D$, or equivalently, if for each $x\in D$ there exists a non-negative integer $n$ such that $nx\in G$.

Title	divisible closure
Canonical name	DivisibleClosure
Date of creation	2013-03-22 15:58:36
Last modified on	2013-03-22 15:58:36
Owner	polarbear (3475)
Last modified by	polarbear (3475)
Numerical id	5
Author	polarbear (3475)
Entry type	Definition
Classification	msc 20K35
Defines	divisible closure of a group