ON BLOCKS OF NORMAL SUBGROUPS OF FINITE GROUPS

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.