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In this paper, we compare the two definitions of Bloch group, and survey theelements 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 Lichtenbaumconjecture on non-Galois fields. By PARI, we get some equations of the zetafunctions on special values and the structure of tame kernel of these fields.

The Bloch groups and special values of Dedekind zeta functions