5 papers
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…
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 -groups over a field implies an isomorphism of the group bases. We explore t…
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…
On commutative tensor factors of group algebras
Diego GarcÃa-Lucas, Ãngel del RÃo, 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.…
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 -groups can have isomorphic modular group algebras was recently answered in the negative by GarcÃa-Lucas, Margolis and del RÃo [J. R…