THE TAME KERNEL OF MULTIQUADRATIC NUMBER FIELDS

Let F/K be a Galois extension of a number field of degree n, (sic)(F) the ring of integers in F, and p a prime number which does not divide n. Let K(2) denote the Milnor K-functor. In this article, we shall study the structure of the odd part of the tame kernel K(2)(sic)(F) of F by using the intermediate fields of F/K. In particular, for a multiquadratic field F, we shall get the p(i)-rank, (i > 0) of K(2)(sic)(F). Finally, we shall determine the structure of the odd parts of K(2)(sic)(F) when F = (sic)(root d, root d(1)), where -100 < d < 0, d(1) = 2, 3, 5, 7.