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

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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

• divisible group
• rational numbers
• rationalization of an abelian group
• rational homotopy type

References

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