On weak commutativity in 𝑝-groups-Reference-Cited by-同舟云学术

On weak commutativity in 𝑝-groups

Published:2023-06-15 Issue:0 Volume:0 Page:
ISSN:1433-5883
Container-title:Journal of Group Theory
language:en
Short-container-title:

Author:

Bastos Raimundo¹,de Melo Emerson¹,de Oliveira Ricardo²,Monetta Carmine³^ORCID

Affiliation:

1. Departamento de Matemática , Universidade de Brasília , Brasilia - DF, 70910-900 Brazil

2. Instituto de Matemática e Estatística , Universidade Federal de Goiás , Goiânia - GO, 74690-900 Brazil

3. Dipartimento di Matematica , Università di Salerno , Via Giovanni Paolo II, 132 – 84084 – Fisciano SA , Italy

Abstract

Abstract The weak commutativity group χ ⁢ ( G )

\chi(G)

is generated by two isomorphic groups 𝐺 and G φ

G^{\varphi}

subject to the relations [ g , g φ ] = 1

[g,g^{\varphi}]=1

for all g ∈ G

g\in G

. We present new bounds for the exponent of χ ⁢ ( G )

\chi(G)

and its sections, when 𝐺 is a finite 𝑝-group.

Publisher

Walter de Gruyter GmbH

Subject

Algebra and Number Theory

Link

https://www.degruyter.com/document/doi/10.1515/jgth-2022-0165/pdf

Reference16 articles.

1. R. Bastos, E. de Melo and R. de Oliveira, On the exponent of the weak commutativity group χ ⁢ ( G ) \chi(G) , Mediterr. J. Math. 18 (2021), no. 5, Paper No. 194.

2. R. Bastos, E. de Melo, N. Gonçalves and R. Nunes, Non-Abelian tensor square and related constructions of 𝑝-groups, Arch. Math. (Basel) 114 (2020), no. 5, 481–490.

3. M. R. Bridson and D. H. Kochloukova, Weak commutativity and finiteness properties of groups, Bull. Lond. Math. Soc. 51 (2019), no. 1, 168–180.

4. M. R. Bridson and D. H. Kochloukova, Weak commutativity, virtually nilpotent groups, and Dehn functions, preprint (2022), https://arxiv.org/abs/2202.0379.

5. G. A. Fernández-Alcober, An introduction to finite 𝑝-groups: regular 𝑝-groups and groups of maximal class, 16th School of Algebra. Part I, Mth. Contemp. 20, Universidade de Brasília, Brasília (2001), 155–226.