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Dihedral Field Extensions of Order 2p Whose Class Numbers are Multiples of p

If L is a cyclic extension of Q of prime degree p, then the class number of L is divisible by p if and only if more than one prime divides the discriminant D, of L. If p ≠ 2, then this condition is equivalent to the existence of more than one cyclic extension of Q of degree p with discriminant equal to D. In this paper we generalize these results to non-galois extensions of Q of degree p whose normal closures have degree 2p over Q.