Nikolaus Conference 2021

Speaker: Diego García Lucas (Murcia)

Title: Non-Isomorphic Finite 2-Groups with Isomorphic Modular Group Algebras


The Modular Isomorphism Problem asks if, given two finite \(p\)-groups \(G\) and \(H\), the existence of an isomorphism between the group algebras \(kG\) and \(kH\) over the field \(k\) with \(p\) elements implies that the groups \(G\) and \(H\) are isomorphic. We solve this problem in the negative by exhibiting a series of pairs of non-isomorphic cyclic-by abelian 2-generated 2-groups such that over each field with characteristic 2 their group algebras are isomorphic. This is a joint work with Leo Margolis and Ángel del Río.

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