13 citations · 42 across the 16 of their papers we have counts for
6 papers · 1 filter
Reciprocity for projective and injective direct summands
Shigeo Koshitani, Taro Sakurai
A reciprocity between multiplicities of projective direct summands for modular group algebras has been known for decades. Recently, the first author extended it to finite-dimension…
On commutative tensor factors of group algebras
Diego García-Lucas, Ángel del Río, Taro Sakurai
We prove that any tensor product factorization with a commutative factor of a modular group algebra over a prime field comes from a direct product decomposition of the group basis.…
The principal -blocks with small numbers of characters
Shigeo Koshitani, Taro Sakurai
For a prime , we determine a Sylow -subgroup of a finite group such that the principal -block of has four irreducible ordinary characters. It has been dete…
The isomorphism problem for group algebras: a criterion
Taro Sakurai
Let be a finite unital commutative ring. We introduce a new class of finite groups, which we call hereditary groups over . Our main result states that if is a hereditary…
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 with where is the number of irreducible ordinary charac…
Central elements of the Jennings basis and certain Morita invariants
Taro Sakurai
From Morita theoretic viewpoint, computing Morita invariants is important. We prove that the intersection of the center and the th (right) socle $ZS^n(A) := Z(A) \cap \operatorn…