Perfect Isometries for Blocks with Abelian Defect Groups and Cyclic Inertial Quotients of Order 4

Abstract

Let b be a p-block of a finite group G with an abelian defect group P and e a root of b in CG(P). If the inertial quotient E (= NG(P, e)/P · CG(P)) is a cyclic group of order 4, 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.