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Computing the tame kernel of quadratic imaginary fields

J. Tate has determined the group K 2 O F (called the tame kernel) for six quadratic imaginary number fields F = Q(√d), where d = -3,-4,-7, -8,-11, -15. Modifying the method of Tate, H. Qin has done the same for d = -24 and d = -35, and M. Skalba for d = -19 and d = -20. In the present paper we discuss the methods of Qin and Skalba, and we apply our results to the field Q(√-23). In the Appendix at the end of the paper K. Belabas and H. Gangl present the results of their computation of K 2 O F for some other values of d. The results agree with the conjectural structure of K 2 O F given in the paper by Browkin and Gangl.