Is the value group of an algebraically closed valued field divisible? Since Every existentially closed abelian group is divisible, I'm trying to show the value group is existentially closed but I don't know how... Even I don't know if the claim holds or not...

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    $\begingroup$ Is the value group of the $p$-adic numbers $\Bbb Q_p$ divisible? $\endgroup$ – Lord Shark the Unknown Oct 20 '18 at 18:54
  • $\begingroup$ So Sorry I forgot to mention ... I meant an algebraically closed valued field... $\endgroup$ – user297564 Oct 21 '18 at 1:12

Yes. If $b$ is a root of $x^n-a$, then $n\cdot v(b) = v(a)$.


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