# Homotopy Type Theory divisible group > history (changes)

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## 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:

$\prod_{n:\mathbb{Z}_{+}} \prod_{g:G} \mathrm{isContr}(\mathrm{fiber}(\alpha(n),g))$

## References

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

Last revised on June 17, 2022 at 20:52:52. See the history of this page for a list of all contributions to it.