On the number of B π′-characters in a nilpotent π-block

Abstract

Broué and Puig set the definition of nilpotent p-blocks, stated the existence of such blocks, and then proved that there is a unique Brauer character in a nilpotent p-block. The present paper, based on the works of Slattery and Robinson, generalizes the above idea to the π-block theory of a π-separable group, defines the nilpotency of a π-block, and proves that there is a unique B π -character in a nilpotent π-block.