Homotopy Type Theory
divisible group > history (Rev #4)
Definition
An abelian group G G is a divisible group if there exists a ℤ + \mathbb{Z}_{+} -action α : ℤ + → ( G → G ) \alpha:\mathbb{Z}_{+} \to (G \to G) , where ℤ + \mathbb{Z}_{+} is the positive integers, such that for all n : ℤ + n:\mathbb{Z}_{+} and all g : G g:G , the fiber of α ( n ) \alpha(n) at g g is contractible :
∏ n : ℤ + ∏ g : G isContr ( fiber ( α ( n ) , g ) ) \prod_{n:\mathbb{Z}_{+}} \prod_{g:G} \mathrm{isContr}(\mathrm{fiber}(\alpha(n),g))
See also
References
Phillip A. Griffith (1970), Infinite Abelian group theory. Chicago Lectures in Mathematics. University of Chicago Press. ISBN 0-226-30870-7
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