Abstract
In this paper, a general architecture has been established for the computation of K2OF, the tame kernel of F, for imaginary cyclic quartic field F=Q(−(D+BD)) with class number one, in particular with large discriminants. As a result, it is proved that K2OF is trivial in the following three cases: B=1, D=2 or B=2, D=13 or B=2, D=29. In the last case, the discriminant of F is 24389. Hence, it can be claimed that the architecture also works for the computation of the tame kernel of a number field with discriminant less than 25000.
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