The 2-Sylow-Subgroup of the Tame Kernel of Number Fields

Abstract

For a number field F with ring of integers OF the tame symbols yield a surjective homomorphism with a finite kernel, which is called the tame kernel, isomorphic to K2(OF). For the relative quadratic extension E/F, where and E ≠ F, let CS(E/ F)(2) denote the 2-Sylow-subgroup of the relative S-class-group of E over F, where S consists of all infinite and dyadic primes of F, and let m be the number of dyadic primes of F, which decompose in E.