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On p-Class Groups of Cyclic Extensions of Prime Degree p of Quadratic Fields

Published online by Cambridge University Press:  26 February 2010

Frank Gerth III
Frank Gerth III
Affiliation:
Department of Mathematics, University of Texas, Austin, Texas 78712, U.S.A.
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Extract

Let Q denote the field of rational numbers, and let p be an odd prime number. Let K be a cyclic extension of Q of degree p, and let a be a generator of Gal (KQ). Let CK denote the p-class group of K (i.e., the Sylow p-subgroup of the ideal class group of K), and let for i = 1, 2, 3, . It is well known that is an elementary abelian p-group of rank tt1, where t is the number of ramified primes in KQ. So we focus our attention on . We let

Type
Research Article
Information
Mathematika , Volume 36 , Issue 1 , June 1989 , pp. 89 - 102
Copyright
Copyright University College London 1989

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