Reduced \(K\)-theory and the group \(G(D)=D^*/F^*D'\) (Q2708728)

Let \(D\) be a finite dimensional division algebra over its center \(F\), \(G(D)=D^*/F^*D'\), where \(D^*=D\setminus\{0\}\) and \(D'\) is the derived group of \(D^*\). Using valuation theory and Platonov's results on reduced \(K\)-theory, the authors investigate some algebraic properties of the group \(G(D)\) which behaves very much like the reduced Whitehead group \(SK_1(D)\). In particular, a stability theorem for \(G(D)\) is given, and \(G(D)\) is computed when \(D\) is a tame and totally ramified valued division algebra. In addition, the authors construct some examples and settle some questions concerning the structure of \(D'\).NEWLINENEWLINEFor the entire collection see [Zbl 0949.00018].