Idempotents in matrix group rings (Q1331913)

Let \(G\) be a group and let \(KG\) be the group algebra of \(G\) over a field \(K\) of characteristic zero. Suppose that \(G\) is a group of finite cohomological dimension \(cd_ K G = n \geq 1\) over \(K\) and \(G\) contains a free abelian subgroup of rank \(n - 1\) in its centre. Let \(E\) be an idempotent matrix with entries in \(KG\). It is proved that the partial augmentations of the trace of \(E\) corresponding to the elements of infinite order are all zero.