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

Let FF be a cubic cyclic field with exactly one ramified prime p,p>7p,p>7, or F=Q(d), a real quadratic field with d≢6(mod9). In this paper, we study the 3-primary part of K2OFK2OF. If 3 does not divide the class number of FF, we get some results about the 9-rank of K2OFK2OF. In particular, in the case of a cubic cyclic field FF with only one ramified prime p>7p>7, we prove that four conclusions concerning the 3-primary part of K2OFK2OF, obtained by J. Browkin by numerical computations for primes pp, 7≤p≤50007≤p≤5000, are true in general.