3 papers
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 is a commutative unital ri…
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 -groups over a field implies an isomorphism of the group bases. We explore t…
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 -groups and that have isomorphic group algebras over the fie…