Nikolaus Conference 2021

Speaker: Leo Margolis (Madrid)

Title: The Modular Isomorphism Problem


The Modular Isomorphism Problem, which had been open for over 50 years, states:

If \(p\) is a prime, \(G\) and \(H\) are finite \(p\)-groups and \(k\) a field of characteristic \(p\), does an isomorphism between the group algebras of \(G\) and \(H\) over \(k\) imply an isomorphism of the groups \(G\) and \(H\)?

The problem has recently been solved by a series of counterexamples, but also various new positive results have been achieved. I will report on these positive results and the methods underlying them.

Joint work with T. Moede, T. Sakurai and M. Stanojkovski.

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