Let $A$ be an abelian group such that for any natural number $n\neq 0$ the multiplication $[n]:A\rightarrow A: a\mapsto n\cdot a$ is surjective. What can we say about $A$ ?
2026-03-30 08:36:45.1774859805
Let $A$ be an abelian group s.t. $\forall n\in\Bbb N, [n]:A\rightarrow A: a\mapsto n\cdot a$ is surjective. What can we say about $A$?
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These are exactly (by definition) the divisible groups. Divisible groups have a number of nice properties, some of which are mentioned at the wiki page.