Tame kernels and second regulators of number fields and their subfields

Abstract Assuming a version of the Lichtenbaum conjecture, we apply Brauer-Kuroda relations between the Dedekind zeta function of a number field and the zeta function of some of its subfields to prove formulas relating the order of the tame kernel of a number fieldFwith the orders of the tame kernels of some of its subfields. The details are given for fieldsFwhich are Galois over ℚ with Galois group the group ℤ/2 × ℤ/2, the dihedral groupD2p;pan odd prime, or the alternating groupA4. We include numerical results illustrating these formulas.