# 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 DivisibleClosure 2013-03-22 15:58:36 2013-03-22 15:58:36 polarbear (3475) polarbear (3475) 5 polarbear (3475) Definition msc 20K35 divisible closure of a group