# Is the value group of an algebraically closed valued field divisible?

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...

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

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