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On the Class Group of an Imaginary Cyclic Field of Conductor 8p and 2-power Degree

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Abstract

Let p = 2e+1q + 1 be an odd prime number with 2 ∤ q. Let K be the imaginary cyclic field of conductor p and degree 2e+1. We denote by F the imaginary quadratic subextension of the imaginary (2; 2)-extension K(√2)/K+ with F ≠ K. We determine the Galois module structure of the 2-part of the class group of F.

Journal

  • Tokyo Journal of Mathematics

    Tokyo Journal of Mathematics 44 (1), 157-173, 2021-01-07

    Project Euclid|Publication Committee for the Tokyo Journal of Mathematics

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