On the center of group algebras in characteristic \(p\) (Q1961997)

Let \(RG\) be the group algebra of a finite group \(G\) over a commutative ring \(R\) of prime characteristic \(p>0\). In this paper the author gives elementary proofs of some results on the central idempotents of \(RG\). For example, he proves that if \(e\) is a central idempotent of \(RG\), then every element of \(\text{Supp }e\) is a \(p'\)-element. Those results are well known when \(R\) is a field. Their classical proof requires the use of a ``lift to characteristic \(0\)''. The new methods explained here are independent of such a lift and work also for a reduced ring of prime characteristic.