Higher G-theory of nilpotent group rings (Q1105668)

Let \(\pi\) be a finite nilpotent group whose Sylow 2-subgroup has no subquotient isomorphic to the quaternion group of order 8, and let R be a left Noetherian ring. A formula is given here for the higher Grothendieck groups of \(R\pi\), analogous to that for \(G_ 0(R\pi)\) given by \textit{H. Lenstra} [J. Pure Appl. Algebra 20, 173-193 (1981; Zbl 0467.16016)]. According to a note added in proof, a similar result is proved by \textit{I. Hambleton}, \textit{L. Taylor} and \textit{E. B. Williams} [J. Algebra 116, No.2, 466-470 (1988)].