On the \(K\)-theory of \({\mathbb{Z}}G\), \(G\) a non-Abelian group of order \(pq\)
type: Item
instance of: scholarly article
title: On the \(K\)-theory of \({\mathbb{Z}}G\), \(G\) a non-Abelian group of order \(pq\)
zbMATH Open document ID: 0639.16016
DOI: 10.1007/BF00536981
author: Reinhard Laubenbacher
published in: \(K\)-Theory
publication date: 1987-01-01T00:00:00Z
review text: 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 \({\mathbb{Z}}G\).
Mathematics Subject Classification ID: 16E20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 18F25
zbMATH DE Number: 4042107
zbMATH Keywords: integral group ring
zbMATH Keywords: long exact sequences
zbMATH Keywords: birelative K-groups
zbMATH Keywords: pullbacks
zbMATH Keywords: G-theory of \({bbfZ}G\)
reviewed by: Michael R. Stein
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4042107