  We prove the "divisible case" of the Milnor-Bloch-Kato conjecture (which is
the first step of Voevodsky's proof of this conjecture for arbitrary prime l)
in a rather clear and elementary way. Assuming this conjecture, we construct a
6-term exact sequence of Galois cohomology with cyclotomic coefficients for any
finite extension of fields whose Galois group has an exact quadruple of
permutational representations over it. Examples include cyclic groups, dihedral
groups, the biquadratic group Z/2\times Z/2, and the symmetric group S_4.
Several exact sequences conjectured by Bloch-Kato, Merkurjev-Tignol, and Kahn
are proven in this way. In addition, we introduce a more sophisticated version
of the classical argument known as "Bass-Tate lemma". Some results about
annihilator ideals in Milnor rings are deduced as corollaries.
