On group invariants determined by modular group algebras: even versus odd characteristic

2022/09/13 by Diego García-Lucas, Ángel del Rı́o, García-Lucas, Diego +3
Mathematics · #Advanced Topics in Algebra #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA) #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.2209.06143

openalex publication_date 2022/09/13 · openalex created_date 2022/09/16 · openalex updated_date 2026/07/28

Abstract

Let p be a an odd prime and let G be a finite p-group with cyclic commutator subgroup G'. We prove that the exponent and the abelianization of the centralizer of G' in G are determined by the group algebra of G over any field of characteristic p. If, additionally, G is 2-generated then almost all the numerical invariants determining G up to isomorphism are determined by the same group algebras; as a consequence the isomorphism type of the centralizer of G' is determined. These claims are known to be false for p=2.

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