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

Diego García-Lucas, Ángel del Río, and Mima Stanojkovski

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Submission date: 14. Sep. 2022
Bibtex
Link to arXiv: See the arXiv entry of this preprint.

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.