The Sylow $p$-Subgroups of Tame Kernels in Dihedral Extensions of Number Fields
Volume 61 / 2013
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 $D_{16}$.
