On theorems of Brauer-Nesbitt and Brandt for characterizations of small block algebras

Shigeo Koshitani, Taro Sakurai

In 1941, Brauer-Nesbitt established a characterization of a block with trivial defect group as a block $B$ with $k(B)=1$ where $k(B)$ is the number of irreducible ordinary charac…