The 2-Sylow subgroups of the tame kernel of imaginary quadratic fields
Volume 69 / 1995
Abstract
1. Introduction. Let F be a number field and the ring of its integers. Many results are known about the group K₂O_F, the tame kernel of F. In particular, many authors have investigated the 2-Sylow subgroup of K₂O_F. As compared with real quadratic fields, the 2-Sylow subgroups of K₂O_F for imaginary quadratic fields F are more difficult to deal with. The objective of this paper is to prove a few theorems on the structure of the 2-Sylow subgroups of K₂O_F for imaginary quadratic fields F. In our Ph.D. thesis (see [11]), we develop a method to determine the structure of the 2-Sylow subgroups of K₂O_F for real quadratic fields F. The present paper is motivated by some ideas in the above thesis.