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MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
28/2022

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

Diego García-Lucas, Ángel del Río and Mima Stanojkovski

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 $p=2$.

Received:
14.09.22
Published:
14.09.22

Related publications

inJournal
2023 Journal Open Access
Diego García-Lucas, Ángel del Río and Mima Stanojkovski

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

In: Algebras and representation theory, 26 (2023) 6, pp. 2683-2707