Let $K$ be an extension of $\mathbb{Q}_p$ and let $L/K$ be a finite extension with $p \nmid e$ where $e = e(L/K)$ is the ramification index of $L/K$. Let $I=I(L/K)$ be the intertia subgroup of $L/K$.
Question Is there a result showing that $I$ must be cyclic?
I still have a vague understanding of things like inertia subgroups, Galois groups over $\mathbb{Q}_p$, etc., so I think a reference to obtain the basics to solve the above question would be the best for me. I don't mind an answer to my question though. Thanks!