3-Blocks with Abelian defect groups isomorphic to $Z_{3^m } \times Z_{3^n } $

Abstract

Let G be a finite group and let p be a fixed prime number. Let B be a p-block of G with defect group D. In this paper, we give results on 3-blocks with abelian defect groups isomorphic to \(Z_{3^m } \times Z_{3^n } \). We are particularly interested in the number of irreducible ordinary characters and the number of irreducible Brauer characters in the block. We calculate two important block invariants k(B) and l(B) in this case.