  In this paper, we compare the two definitions of Bloch group, and survey the
elements in Bloch group. We confirm the Lichtenbaum conjecture on the field
$Q(\zeta_p)$ under the assumption the truth of the base of the Bloch group of
$Q(\zeta_p)$ and the relations of $K_2$ group. We also study the Lichtenbaum
conjecture on non-Galois fields. By PARI, we get some equations of the zeta
functions on special values and the structure of tame kernel of these fields.
