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On weak commutativity in 𝑝-groups

  • Raimundo Bastos , Emerson de Melo , Ricardo de Oliveira and Carmine Monetta ORCID logo EMAIL logo
Published/Copyright: June 15, 2023

Abstract

The weak commutativity group χ ( G ) is generated by two isomorphic groups 𝐺 and G φ subject to the relations [ g , g φ ] = 1 for all g G . We present new bounds for the exponent of χ ( G ) and its sections, when 𝐺 is a finite 𝑝-group.

Funding statement: This work was partially supported by DPI/UnB and FAPDF (Brazil), and by a grant of the University of Campania “Luigi Vanvitelli”, in the framework of the project GoAL (V:ALERE 2019). The last named author was supported by the “National Group for Algebraic and Geometric Structures, and their Applications” (GNSAGA – INdAM).

Acknowledgements

The authors wish to thank the anonymous referee for their insightful comments. Moreover, this study was carried out during a visit of the last named author to the University of Brasilia. He wishes to thank the Department of Mathematics for the excellent hospitality.

  1. Communicated by: Dessislava Kochloukova

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Received: 2022-09-19
Revised: 2023-01-26
Published Online: 2023-06-15
Published in Print: 2023-11-01

© 2023 Walter de Gruyter GmbH, Berlin/Boston

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