PERFECT ISOMETRIES FOR PRINCIPAL BLOCKS WITH ABELIAN DEFECT GROUPS AND ELEMENTARY ABELIAN 2-INERTIAL QUOTIENTS

摘要

Let b be the principal 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 an elementary abelian 2-group (respectively, a dihedral group of order 8) and p not equal 3, then b and its Brauer correspondent, considered as blocks of G and N-G(P) are isotypic and, in particular, there is a perfect isometry between them. (C) 1997 Academic Press. [References: 19]