On the \(K\)-theory of \({\mathbb{Z}}G\), \(G\) a non-Abelian group of order \(pq\) (Q1100259)

L. Klingler, building on earlier work of L. Levy, showed how the integral group ring of a non-abelian group G of order pq, p and q distinct primes with \(q| p-1\), can be constructed as a multiple pullback ring. The author exploits techniques he developed in an earlier paper to describe the K-theory of \({\mathbb{Z}}G\) in terms of long exact sequences involving birelative K-groups and the K-theory of simpler rings which turn up in the pullbacks. These reduce the computation of \(K_*({\mathbb{Z}}G)\), modulo extension questions, to the computation of the birelative K-groups. In addition, he gives an alternate derivation of a theorem of D. Webb describing the G-theory of \({\mathbb{Z}}G\).