Clifford Theory of a Finite Group that Contains a Defect 0 p-Block of a Normal Subgroup

Abstract

Let G be a finite group with a normal subgroup N that has a p-block b of defect 0. As is well-known, we may assume that b is G-stable. Then we show that there is an extension of G/N by a central cyclic p′-subgroup and a p-block of such that the blocks of G covering b biject with the blocks of that cover and corresponding blocks have several equivalent properties. These results extend the known results in the situation that N is a normal p′-subgroup.