Integral group rings with Jordan decomposition
The authors investigate Jordan decomposition for elements \(x\) of the integral group ring \(\mathbb{Z} G\) of a finite group \(G\). If \(x\) is written as the sum \(s+n\) of commuting elements \(s\) and \(n\) of the rational group algebra \(\mathbb{Q} G\), where \(s\) is semisimple and \(n\) nilpotent, then one says that Jordan decomposition holds in \(\mathbb{Z} G\) if \(s\) and \(n\) necessarily lie in \(\mathbb{Z} G\) for all \(x\) in \(\mathbb{Z} G\). The authors characterize all finite groups \(G\) for which Jordan decomposition holds in \(\mathbb{Z} G\).
scientific article; zbMATH DE number 4139957