A note on the Glauberman-Watanabe corresponding blocks of finite groups with normal defect groups

Abstract

Harris proved that there is an indecomposable bimodule with a trivial source which induces a Morita equivalence between Glauberman-Watanabe corresponding block algebras of finite groups with normal defect groups and the Glauberman correspondence of characters in corresponding blocks. We note an implication of the Puig correspondence in the conext of the Glauberman-Watanabe correspondence and then, using this, show Harris's theorem in two ways.