Abstract
Let K 1 and K 2 be number fields and F = K 1 ⋔ K 2 . Suppose K 1 F and K 2 F are of prime degree p but are not necessarily normal. Let N 1 and N 2 be the normal closures of K 1 and K 2 over F, respectively, L = K 1 K 2, N = N 1 N 2, and B be a prime divisor of N which divides p and is totally ramified in K 1 F and K 2 F . Let N L be the ramification index of B in N L , t L F be the total ramification number of B in L F , and t= min{t K 1 F , t K 2 F } . Then M ( K 1, K 2) is exactly divisible by B M , where M = e N L [e L K 1 (t + 1) 2 − t L F ] .
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