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An online session of the Algebra and Logic Seminar will be held on May 13, 2022 (Friday) at 1:00 pm (UTC+3).

A talk on:

A counterexample to the modular isomorphism problem

will be delivered by Diego García-Lucas (Universidad de Murcia, Spain).

Abstract. The modular isomorphism problem asks whether the isomorphism type of the modular group algebra of a p-group G over a field of characteristic p determines the isomorphism type of G. It was explicitly mentioned in a survey by Richard Brauer in 1963, and was the only classical version of the isomorphism problem for group rings which had resisted a solution, though it received considerable attention. Several partial positive solutions were obtained imposing very strong conditions on the group G, for instance the one of being metacyclic.

In a joint work with Leo Margolis and Ángel del Río, we solve the modular isomorphism problem in the negative by exhibiting a series of pairs of non-isomorphic 2-groups with isomorphic modular group algebras over every field of characteristic 2. These groups are two-generated with cyclic derived subgroup. We will also discuss the (lack of) possibility of obtaining, in a naive way, analogues to the counterexamples for p > 2 verifying this condition.


The seminar will be held via Zoom and anyone can join at:


Topic: Онлайн семинар на секция “Алгебра и логика”
Time: May 13, 2022 01:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647

Algebra and Logic Department, IMI-BAS
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