The question is:
Let L / K be a finite (not necessarily Galois) extension of algebraic number fields and N / K the normal closure of L / K. Show that a prime ideal p of K is totally split in L if and only if it is totally split in N. Hint: Use the double coset decomposition H\G/GP, where G = G(N/K), H = G(N/L) and GP , is the decomposition group of a prime ideal P over p.
My question is how to use this hint to solve this problem; please give me some advice.