Non-isomorphic 2-groups with isomorphic modular group algebras

2021/06/14 by García, Diego, Margolis, Leo, del Río, Ángel · 2 citations
#16S34 #16U60 #20C05 #20D15 #FOS: Mathematics #Group Theory (math.GR) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2106.07231

Abstract

We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.

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• Stable equivalence of Morita type and quotient fusion system
• Where isomorphisms of group algebras fail to lift

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