The 3-Sylow subgroup of the tame kernel of real number fields

Let F be a cubic cyclic field with exactly one ramified prime p, p > 7, or F a real quadratic field with d not equivalent to 6 (mod 9). In this paper, we study the 3-primary part of K2OF. If 3 does not divide the class number of F, we get some results about the 9-rank of K2OF. In particular, in the case of a cubic cyclic field F with only one ramified prime p > 7, we prove that four conclusions concerning the 3-primary part of K2OF, obtained by J. Browkin by numerical computations for primes p, 7 <= p <= 5000, are true in general. (c) 2006 Elsevier B.V. All rights reserved.