On the Generation of the Tame Kernel by Dennis-Stein Symbols Original Research Article

Let p be an odd prime number and let F be a number field not containing a primitive pth root of unity ζp. In this paper we show that if p[formula] [F : image] · disc(F) then the p-primary part of K2(imageF[1/p]) is generated by Dennis-Stein symbols. For the real quadratic fields F = image([formula]) and F = image([formula]) we compute generators for the tame kernel K2(imageF) and give presentations for SLn(imageF) (n ≥ 3) for both fields.