Homotopy Type Theory divisible group > history (Rev #1)

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:

Properties

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

See also

• abelian 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