Editing Divisible group (section)

==Examples==

* The [[rational number]]s <math>\mathbb Q</math> form a divisible group under addition.
* More generally, the underlying additive group of any [[vector space]] over <math>\mathbb Q</math> is divisible.
* Every [[quotient group|quotient]] of a divisible group is divisible. Thus, <math>\mathbb Q/\mathbb Z</math> is divisible.
* The ''p''-[[primary component]] <math>\mathbb Z[1/p]/\mathbb Z</math> of <math>\mathbb Q/ \mathbb Z</math>, which is [[group isomorphism|isomorphic]] to the ''p''-[[quasicyclic group]] <math>\mathbb Z[p^\infty]</math>, is divisible.
* The multiplicative group of the [[complex number]]s <math>\mathbb C^*</math> is divisible.
* Every [[existentially closed]] abelian group (in the [[model theory|model theoretic]] sense) is divisible.