Homotopy Type Theory divisible group > history (Rev #3)

Definition

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