Perfect Isometries for Principal Blocks with Abelian Defect Groups and Elementary Abelian 2-Inertial Quotients Original Research Article

Letbbe the principalp-block of a finite groupGwith an abelian defect groupPandea root ofbinCG(P). If the inertial quotientE( = NG(P, e)/P · CG(P)) is an elementary abelian 2-group (respectively, a dihedral group of order 8) andp ≠ 3, thenband its Brauer correspondent, considered as blocks ofGandNG(P) are isotypic and, in particular, there is a perfect isometry between them.