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 image, a real quadratic field with image. In this paper, we study the 3-primary part of image. If 3 does not divide the class number of F, we get some results about the 9-rank of image. 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 image, obtained by J. Browkin by numerical computations for primes p, 7≤p≤5000, are true in general.