On p-blocks with abelian defect groups and inertial index 2 or 3, I

Abstract

Let G be a finite group and B be a p-block of G with an abelian defect group and inertial index e. If e = 2, then the number of irreducible Brauer characters in B is 2. If p ≠ 2 and e = 3, then the number of irreducible Brauer characters in B is 3. The number of irreducible ordinary characters in B is also determined in both cases.