Geodesic
Dihedral Field Extensions of Order 2p Whose Class Numbers are Multiples of p
Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 429-439

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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. 
Callahan, T. Dihedral Field Extensions of Order 2p Whose Class Numbers are Multiples of p. Canadian journal of mathematics, Tome 28 (1976) no. 2, pp. 429-439. doi: 10.4153/CJM-1976-043-x
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