Homotopy Type Theory divisible group > history (Rev #5)

Definition

An abelian group $G$ is a divisible group if there exists a multiplicative $\mathbb{Z}_{+}$-action $\alpha:\mathbb{Z}_{+} \to (G \to G)$, where $\mathbb{Z}_{+}$ is the positive integers, such that for all $n:\mathbb{Z}_{+}$ and all $g:G$, the fiber of $\alpha(n)$ at $g$ is contractible:

See also

• abelian group
• rational numbers
• torsion-free divisible group

References

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