#
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?.

## See also

## References

- Phillip A. Griffith (1970), Infinite Abelian group theory. Chicago Lectures in Mathematics. University of Chicago Press. ISBN 0-226-30870-7

Revision on June 15, 2022 at 23:03:57 by
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