Tame kernels of cubic and sextic fields

Abstract

Let K be a non-Galois cubic field, and let F denote the normal closure of K/Q or a sextic cyclic field. In this paper, we establish some relations between the p-rank of K2OK (resp. K2OF) and the p-rank of the ideal class groups of some subfields of K(ζp) (resp. F(ζp)). In the case of p=3, we obtain estimates for the p-ranks of tame kernels K2OK (resp. K2OF).