# Homotopy Type Theory torsion-free divisible group > history (Rev #4)

## Definition

A divisible group $G$ is torsion-free if the only integer $n:\mathbb{Z}$ such that $\alpha(n)(g) = 0$ for all $g:G$ is $0$.

## Properties

• Just as every abelian group is a $\mathbb{Z}$-module, every torsion-free divisible group is a $\mathbb{Q}$-module, or a $\mathbb{Q}$-vector space?.