The following exercise and hint appear in Neukirch's Algebraic Number Theory (Section 9, Exercise 3, page 58)
Let $L/K$ be a solvable extension of prime degree $p$ (not necessarily Galois). If the unramified prime ideal $\mathfrak{p}$ in $L$ has two prime factors $\mathfrak{P}$ and $\mathfrak{P'}$ of degree 1, then it is already totally split (theorem of F.K. Schmidt).
Neukirch also gives this hint:
If $G$ is a transitive solvable permutation group of prime degree $p$, then there is no nontrivial permutation $\sigma \in G$ which fixes two distinct letters.
Can we use the conclusion of my former question to solve this one? Thanks!
I would like to know how to use "Let $L/K$ be a solvable extension of prime degree $p$".
P.S. I'm new here and I've asked my friend Roun to ask the "former question" for me.