The functor K2 for multiquadratic number fields

Abstract

Let F and 0 F be a number field and its ring of integers respectively. Let K 2 denote Milnor K-functor. In the paper we describe the structure of the group K 2Of/R2F, where F is the Hilbert kernel and F is multiquadratic extension of the rational number field. Moreover, we give some characterization o f fields with trivial group K 2Of/R2F. At the end we make some remarks on p-rank o f K 2Of and divisibility of the ideal class group by 2.