The Sylow $p$-Subgroups of Tame Kernels in Dihedral Extensions of Number Fields

Volume 61 / 2013

Qianqian Cui, Haiyan Zhou Bulletin Polish Acad. Sci. Math. 61 (2013), 113-121 MSC: 11R70, 12F10. DOI: 10.4064/ba61-2-4

Abstract

Let $F/E$ be a Galois extension of number fields with Galois group $D_{2^{n}}$. In this paper, we give some expressions for the order of the Sylow $p$-subgroups of tame kernels of $F$ and some of its subfields containing $E$, where $p$ is an odd prime. As applications, we give some results about the order of the Sylow $p$-subgroups when $F/E$ is a Galois extension of number fields with Galois group $D_{16}$.

Authors

  • Qianqian CuiSchool of Mathematical Sciences
    Nanjing Normal University
    Nanjing, 210023
    P.R. China
    e-mail
  • Haiyan ZhouSchool of Mathematical Sciences
    Nanjing Normal University
    Nanjing, 210023
    P.R. China
    e-mail

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