The Modular Isomorphism Problem: a survey

Abstract

The Modular Isomorphism Problem asks if an isomorphism of group algebras of two finite p-groups G and H over a field of characteristic p, implies an isomorhism of the groups G and H. We survey the history of the problem, explain strategies which were developed to study it and present the recent negative solution of the problem. The problem is also compared to other isomorphism problems for group rings and various question remaining open are included.

arXiv comment32 pages. Minor changes and corrections. More general formulation at beginning of Section 7

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Cited by in corpus (2)

• On twisted group ring isomorphism problem for p-groups
• The Modular Isomorphism Problem over all fields