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Questions tagged [divisible-groups]

For questions about the structure and properties of a divisible group, which are Abelian groups in which one can "divide" by positive integers.

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universal nonabelian divisible group

For this post, a group $G$ shall be referred to as generally divisible, in case $\forall{x\in G:}~\forall{n\in\mathbb{N}^{\times}:}~\exists{y\in G:}~y^{n}=x$. Note. Here is no commutativity ...
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Structure theorem for divisible modules

I would like to know if there is some analogue theorem of structure for divisible modules as there is for divisible abelian groups. More exactly, given a divisible $R$-module $M$, where $R$ is a PID, ...