On blocks of normal subgroups of finite groups

Abstract

For a block $b$ of a normal subgroup of a finite group $G$, E.C. Dade has defined a subgroup $G[b]$ of $G$. We give a character-theoretical interpretation of his result on $G[b]$. In the course of proofs we determine a defect group of a block of $G[b]$ covering $b$. We also consider character-theoretical characterizations of isomorphic blocks with respect to normal subgroups.