4 papers · 1 filter
Elementary divisors of the Cartan matrix for partial characters
Kaveh Dastouri, Taro Sakurai
Let be a set of primes and let be a finite -separable group. We prove that the Cartan matrix for the -partial characters of is equivalent over the integers to…
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 is a commutative unital ri…
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 -groups and that have isomorphic group algebras over the fie…
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…