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Abstract

1. Introduction. Let F be a number field and $O_F$ 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.