A reduction theorem for the Isomorphism Problem of group algebras over fields

We prove that the Isomorphism Problem for group algebras reduces to group algebras over finite extensions of the prime field. In particular, the Modular Isomorphism Problem reduces to finite modular group algebras.& COPY; 2023 Elsevier B.V. All rights reserved.

Automated summary

This article proves that the Isomorphism Problem for group algebras can be reduced to group algebras over finite extensions of the prime field. In particular, the Modular Isomorphism Problem can be reduced to finite modular group algebras.