Homotopy Type Theory
divisible group > history (Rev #3)
Definition
An abelian group G G is a divisible group if there exists a left ℤ + \mathbb{Z}_{+} -action ( − ) ( − ) : ℤ + × G → G (-)(-):\mathbb{Z}_{+} \times G \to G , where ℤ + \mathbb{Z}_{+} is the positve integers, such that for all n : ℤ + n:\mathbb{Z}_{+} and all g : G g:G , the fiber of n ( − ) n(-) at g g is contractible :
∏ n : ℤ + ∏ g : G isContr ( fiber ( n ( − ) , g ) ) \prod_{n:\mathbb{Z}_{+}} \prod_{g:G} \mathrm{isContr}(\mathrm{fiber}(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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