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

  • Frank Gerth (a1)
  • DOI: http://dx.doi.org/10.1112/S0025579300013590
  • Published online: 01 February 2010
Abstract

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

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This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

3.A. Frohlich . Central Extensions, Galois Groups, and Ideal Class Groups of Number Fields (American Mathematical Society, Providence, R.I., 1983).

5.F. Gerth . An application of matrices over finite fields to algebraic number theory. Math. Comp., 41 (1983), 229234.

6.F. Gerth . Limit probabilities for coranks of matrices over GF((q). Linear and Multilinear Algebra, 19 (1986), 7993.

7.F. Gerth . Densities for ranks of certain parts of p-class groups. Proc. Amer. Math. Soc., 99 (1987), 18.

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Mathematika
  • ISSN: 0025-5793
  • EISSN: 2041-7942
  • URL: /core/journals/mathematika
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