Lower defect groups and vertices of simple modules

Abstract

We compare lower defect groups associated with $p$-regular classes and vertices of simple modules for a block of a finite group algebra. We show that lower defect groups are contained in vertices of simple modules after suitable reordering. Moreover, for a block of principal type, we show that a $p$-regular lower defect group which contains a vertex of simple module is a defect group of the block.

10 pages