On \(SG_ n\) of orders
Let R be a Dedekind domain with field of fractions K, and let M be an R- order in a separable K-algebra A. The authors prove that, under certain conditions on R and M, \(SG_ n(M)=\ker (G_ n(M)\to G_ n(A))=0\) for all \(n\geq 1\). This generalizes a result of \textit{C. Soulé} [Invent. Math. 55, 251-295 (1979; Zbl 0437.12008)]. In particular, this theorem applies to the integral group ring of a finite group, i.e., \(SG_ n(RG)=0\) if G is a finite group and R is the ring of integers in a number field. When M is regular, e.g., when M is maximal, then \(SK_ n(M)=0\) for all \(n\geq 1\).
scientific article; zbMATH DE number 4148335
scientific article