PERFECT ISOMETRIES AND ISOTYPIES FOR BLOCKS WITH ABELIAN DEFECT GROUPS AND THE INERTIAL QUOTIENTS ISOMORPHIC TO Z(4)XZ(2)

摘要

Let b be a p-block of a finite group G with 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 isomorphic to Z(4) x Z, and p greater than or equal to 7, then there is a perfect isometry from the group of generalized characters of some twisted group algebra of the semidirect product of E and P onto the group of generalized characters of G in b, and, furthermore, b and its Brauer correspondent in N-G(P) are isotypic. (C) 1996 Academic Press, Inc. [References: 14]