On the Number of Ordinary Irreducible Characters in a p-Block with a Minimal Nonabelian Defect Group

Abstract

In this article, we give some new results on the block with a minimal nonabelian matacyclic defect group of odd order. First, we verify Brauer's k(B)-conjecture and Olsson's k 0(B)-conjecture. Then we give the number of irreducible ordinary and modular characters in the block provided that it has a normal defect group. Moreover, we calculate k(B) − l(B) without the hypothesis on normality when the block B has a nonabelian defect group with a cyclic maximal subgroup.