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

Published online by Cambridge University Press:  20 November 2018

T. Callahan
T. Callahan*
Affiliation:
University of Toronto, Toronto, Ontario
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 2 , 01 April 1976 , pp. 429 - 439
Copyright
Copyright © Canadian Mathematical Society 1976

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