# Darstellungstheorietage and Nikolaus Conference 2021

Speaker: Diego García Lucas (Murcia)

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

Abstract:

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.