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

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Definition

An abelian group $G$ is a divisible group if there exists a left$\mathbb{Z}_{+}$-action $(\alpha -)(-):{\mathbb{Z}}_{+}<span><del\; class="diffmod">\; \times </del><ins\; class="diffmod">\; \to </ins></span>(G\to G)$ (-)(-):\mathbb{Z}_{+} \alpha:\mathbb{Z}_{+} \times G \to G (G \to G), where $\mathbb{Z}_{+}$ is the positve positive integers, such that for all$n:\mathbb{Z}_{+}$ and all $g:G$, the fiber of $\mathrm{<span><del\; class="diffmod">\; n</del><ins\; class="diffmod">\; \alpha </ins></span>}(-n)$ n(-) \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