On 2-Sylow subgroups of tame kernels of certain quadratic fields (Q2732541)

Let \(F={\mathbb Q} (\sqrt d)\) be a quadratic number field, where \(d\) has only 2 odd prime factors, and \(2\in N(F)\). The author gives conditions for the 4-rank and 8-rank of the tame kernel \(K_2 O_F\) to be zero, where \(O_F\) is the ring of integers of \(F\). For example, when \(d=pq\), \(p\equiv q \equiv 1\pmod 8\), then the 4-rank is zero if and only if 8 divides the class number of \({\mathbb Q} (\sqrt{-pq})\). These results supplement [\textit{H. Qin}, Acta Arith. 72, 323-333 (1995; Zbl 0834.11050)].