Perfect Isometries for Blocks with Abelian Defect Groups and Klein Four Inertial Quotients

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 C G ( P). If the inertial quotient E (= N G ( P, e)/ C G ( P)) is a Klein four group, there is a so called perfect isometry from the group of generalized characters of a suitable twisted group algebra of the semidirect product of E and P onto the group of generalized characters of G in b.