For a prime number $p$, $F_{p}$ is the p-adic number groups and $J_{p}$ is the p-adic integer groups. Is $F_{p}$, the minimal divisible extension of $J_{p}$?
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Divisible group extension, or divisible $J_p$-algebra extension? – Alex Youcis Aug 21 '13 at 04:12
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I don't know what a minimal divisible extension is, but I do know that every $p$-adic number $q$ is the unique solution to $p^n q=z$ for some natural number $n$ and $p$-adic integer $z$. So no proper subgroup of the $p$-adic numbers containing the $p$-adic integers is divisible. – Chris Culter Aug 21 '13 at 05:22