Vol. 296, No. 2, 2018

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Presentations of generalisations of Thompson's group V

Conchita Martínez-Pérez, Francesco Matucci and Brita Nucinkis

Vol. 296 (2018), No. 2, 371–403

We consider generalisations of Thompson’s group V, denoted by V r(Σ), which also include the groups of Higman, Stein and Brin. We showed earlier (Forum Math. 28:5 (2016), 909–921) that under some mild conditions these groups and centralisers of their finite subgroups are of type F. Under more general conditions we show that the groups V r(Σ) are finitely generated and, under the mild conditions mentioned above for which they are of type F and hence finitely presented, we give a recipe to find explicit presentations. For the centralisers of finite subgroups we find a suitable infinite presentation and then show how to apply a general procedure to shorten this presentation. In the appendix, we give a proof of this general shortening procedure.

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generalized Thompson groups, finite presentations
Mathematical Subject Classification 2010
Primary: 20J05
Received: 17 January 2017
Revised: 12 December 2017
Accepted: 12 December 2017
Published: 16 July 2018
Conchita Martínez-Pérez
Departamento de Matemáticas
Universidad de Zaragoza
Francesco Matucci
Instituto de Matemática, Estatística e Computação Científica
Universidade Estadual de Campinas
Brita Nucinkis
Department of Mathematics
Royal Holloway
University of London
United Kingdom