Perfect Isometries for Blocks with Abelian Defect Groups and Dihedral Inertial Quotients of Order 6 Original Research Article

Let b be a p-block of a finite group G with an abelian defect group P and let e be a root of b in CG(P). If the inertial quotient E (= NG(P, e)/P · CG(P)) is a dihedral group of order 6, then there is a perfect isometry from the group of generalized characters of the group algebra of the semidirect product of E and P onto the group of generalized characters of G in b.