Let $K$ be a finite extension of $\mathbb{Q}_p$ with ramification index $e$.
Then we have $v(\pi)=\frac{1}{e}$, where $\pi$ is the uniformizer in the ring of integers $O_K$ of $K$.
Let $b \in K$ be an element of $K$ such that $v(b)=\frac{1}{e'}$.
Is always $e' \mid e$ true ?
The value group of $K$ is $\frac{1}{e} \mathbb{Z}$. But $\frac{1}{e} \mathbb{Z}$ must as well contain $\frac{1}{e'}$, and this holds if and only if $e' \mid e$.
Is it true ?