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Embedding right-angled Artin groups into Brin–Thompson groups

Part of: Structure and classification of infinite or finite groups Special aspects of infinite or finite groups

Published online by Cambridge University Press:  23 April 2019

JAMES BELK ,
COLLIN BLEAK  and
FRANCESCO MATUCCI
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
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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.

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 20F36: Braid groups; Artin groups 20E07: Subgroup theorems; subgroup growth
Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 169 , Issue 2 , September 2020 , pp. 225 - 229
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).

References

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