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Embedding right-angled Artin groups into Brin–Thompson groups

Published online by Cambridge University Press:  23 April 2019

JAMES BELK
Affiliation:
University of St Andrews e-mail: jmb42@st-andrews.ac.uk
COLLIN BLEAK
Affiliation:
University of St Andrews e-mail: jmb42@st-andrews.ac.uk
FRANCESCO MATUCCI
Affiliation:
University of Campinas e-mail: francesco@ime.unicamp.br

Abstract

We prove that every finitely-generated right-angled Artin group embeds into some Brin–Thompson group nV. It follows that any virtually special group can be embedded into some nV, a class that includes surface groups, all finitely-generated Coxeter groups, and many one-ended hyperbolic groups.

Type
Research Article
Copyright
© Cambridge Philosophical Society 2019

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Footnotes

The first and second authors have been partially supported by EPSRC grant EP/R032866/1 during the creation of this paper.

The third author is a member of the Gruppo Nazionale per le Strutture Algebriche, Geometriche e le loro Applicazioni (GNSAGA) of the Istituto Nazionale di Alta Matematica (INdAM) and gratefully acknowledges the support of the Fundação para a Ciência e a Tecnologia (FCT projects UID/Multi/04621/2013 (CEMAT-Ciências) and PEst-OE/MAT/UI0143/2014).

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