�ber die Gr�sse des Radikals in Gruppenringen �ber der symmetrischen Gruppe

Abstract

Let denote the symmetric group of order n!, K a field of characteristic p>0, and Ra(K ) the radical of the group algebra K . In this paper it is shown that the quotient of the K-dimension of Ra(K ) and the K-dimension of K tends to 1, if n increases indefinitely. To prove this, I will use a correspondence between the indecomposable direct summands of K and the p-regular diagramms. Then by a detailed study of the hookgraphs of p-regular diagramms we obtain the result.