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On the modular isomorphism problem for groups of nilpotency class 2 with cyclic center

  • Diego García-Lucas ORCID logo and Leo Margolis EMAIL logo
Published/Copyright: January 2, 2024

Abstract

We show that the modular isomorphism problem has a positive answer for groups of nilpotency class 2 with cyclic center, i.e., that for such p-groups G and H an isomorphism between the group algebras FG and FH implies an isomorphism of the groups G and H for F the field of p elements. For groups of odd order this implication is also proven for F being any field of characteristic p. For groups of even order we need either to make an additional assumption on the groups or on the field.

MSC 2020: 16U60; 16S34; 20C05

Communicated by Manfred Droste


Award Identifier / Grant number: PID2020-113206GB-I00

Funding statement: The first author acknowledges support by Grant PID2020-113206GB-I00 funded by MCIN/AEI and Grant Fundación Séneca 22004/PI/22 and the second by the Spanish Ministry of Science and Innovation, through the Severo Ochoa Programme for Centres of Excellence in R&D (CEX2019-000904-S) and through the Ramon y Cajal grant program.

Acknowledgements

We would like to thank Ángel González Prieto for discussions on how to attack Problem 5.6.

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Received: 2023-06-24
Revised: 2023-10-26
Published Online: 2024-01-02
Published in Print: 2024-09-01

© 2024 Walter de Gruyter GmbH, Berlin/Boston

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