PERFECT ISOMETRIES FOR BLOCKS WITH ABELIAN DEFECT GROUPS AND CYCLIC INERTIAL QUOTIENTS OF ORDER 4

摘要

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)/P . C-G(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. (C) 1995 Academic Press, Inc. [References: 11]