Taro Sakurai

activity

20162026

most citedThe isomorphism problem for group algebras: a criterion

13 citations · 42 across the 16 of their papers we have counts for

collaborators

18 papers

math.RT2026

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…

math.RA2026

Tensor factorization of local algebras

Taro Sakurai

Let $A$ be a finite-dimensional local algebra over a splitting field. We prove that an irreducible tensor factorization $A ≅ P_{1} \otimes \dots \otimes P_{n}$ of the algebra $A$ …

math.GR2026

Elementary divisors of the Cartan matrix for partial characters

Kaveh Dastouri, Taro Sakurai

Let $π$ be a set of primes and let $G$ be a finite $π$ -separable group. We prove that the Cartan matrix $C$ for the $π$ -partial characters of $G$ is equivalent over the integers to…

math.GR2026

Geometric approach to the modular isomorphism problem: groups of order 64

Leo Margolis, Taro Sakurai

We introduce a procedure based on computational algebraic geometry to determine whether two algebras are isomorphic. We then apply it to show that if $R$ is a commutative unital ri…

math.GR2025

Where isomorphisms of group algebras fail to lift

Leo Margolis, Taro Sakurai

Counterexamples to the Modular Isomorphism Problem were discovered recently. These are non-isomorphic finite $2$ -groups $G$ and $H$ that have isomorphic group algebras over the fie…

math.RA2025

The Modular Isomorphism Problem over all fields

Leo Margolis, Taro Sakurai

The Modular Isomorphism Problem asks, if an isomorphism between modular group algebras of finite $p$ -groups over a field $F$ implies an isomorphism of the group bases. We explore t…

math.RT2024

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.…

math.RA2024★ 2 cited

Identification of non-isomorphic 2-groups with dihedral central quotient and isomorphic modular group algebras

Leo Margolis, Taro Sakurai

The question whether non-isomorphic finite $p$ -groups can have isomorphic modular group algebras was recently answered in the negative by García-Lucas, Margolis and del Río [J. Rei…

math.CO2022

Counting cliques in a random graph

Taro Sakurai, Norihide Tokushige

We show that the expected number of cliques in the Erdős-Rényi random graph $G (n, p)$ is $n^{\frac{1}{- 2 l o g p} (l o g n - 2 l o g l o g n + O (1))}$ .

math.RA2021

Abelian invariants and a reduction theorem for the modular isomorphism problem

Leo Margolis, Taro Sakurai, Mima Stanojkovski

We show that elementary abelian direct factors can be disregarded in the study of the modular isomorphism problem. Moreover, we obtain four new series of abelian invariants of the…

cs.AI2021★ 4 cited

On formal concepts of random formal contexts

Taro Sakurai

In formal concept analysis, it is well-known that the number of formal concepts can be exponential in the worst case. To analyze the average case, we introduce a probabilistic mode…

math.RT2020★ 8 cited

The principal $p$ -blocks with small numbers of characters

Shigeo Koshitani, Taro Sakurai

For a prime $p$ , we determine a Sylow $p$ -subgroup $D$ of a finite group $G$ such that the principal $p$ -block $B$ of $G$ has four irreducible ordinary characters. It has been dete…

math.GR2020★ 4 cited

Finite groups with very few character values

Taro Sakurai

Finite groups with very few character values are characterized. The following is the main result of this article: a finite non-abelian group has precisely four character values if…

math.RT2019★ 13 cited

The isomorphism problem for group algebras: a criterion

Taro Sakurai

Let $R$ be a finite unital commutative ring. We introduce a new class of finite groups, which we call hereditary groups over $R$ . Our main result states that if $G$ is a hereditary…

cs.IT2018★ 6 cited

An explicit formula for a weight enumerator of linear-congruence codes

Taro Sakurai

An explicit formula for a weight enumerator of linear-congruence codes is provided. This extends the work of Bibak and Milenkovic [IEEE ISIT (2018) 431-435] addressing the binary c…

math.RT2018

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…

math.RT2017★ 3 cited

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 $n$ th (right) socle $ZS^n(A) := Z(A) \cap \operatorn…

math.RA2016★ 2 cited

A generalization of dual symmetry and reciprocity for symmetric algebras

Taro Sakurai

Slicing a module into semisimple ones is useful to study modules. Loewy structures provide a means of doing so. To establish the Loewy structures of projective modules over a finit…

Reciprocity for projective and injective direct summands

Tensor factorization of local algebras

Elementary divisors of the Cartan matrix for partial characters

Geometric approach to the modular isomorphism problem: groups of order 64

Where isomorphisms of group algebras fail to lift

The Modular Isomorphism Problem over all fields

On commutative tensor factors of group algebras

Identification of non-isomorphic 2-groups with dihedral central quotient and isomorphic modular group algebras

Counting cliques in a random graph

Abelian invariants and a reduction theorem for the modular isomorphism problem

On formal concepts of random formal contexts

The principal p-blocks with small numbers of characters

Finite groups with very few character values

The isomorphism problem for group algebras: a criterion

An explicit formula for a weight enumerator of linear-congruence codes

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

Central elements of the Jennings basis and certain Morita invariants

A generalization of dual symmetry and reciprocity for symmetric algebras

The principal $p$ -blocks with small numbers of characters