Non-isomorphic 2-groups with isomorphic modular group algebras

TL;DR

This paper demonstrates that there exist non-isomorphic finite 2-groups whose group algebras are isomorphic over any field of characteristic 2, resolving the longstanding Modular Isomorphism Problem.

Contribution

It provides explicit examples of non-isomorphic 2-groups with isomorphic modular group algebras, settling the Modular Isomorphism Problem.

Findings

Existence of non-isomorphic 2-groups with isomorphic modular group algebras

Resolution of the Modular Isomorphism Problem for 2-groups

Applicable over any field of characteristic 2

Abstract

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.