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CONJUGATING AUTOMORPHISMS OF GRAPH PRODUCTS: KAZHDAN’S PROPERTY (T) AND SQ-UNIVERSALITY

Part of: Graph theory Special aspects of infinite or finite groups

Published online by Cambridge University Press:  07 August 2019

ANTHONY GENEVOIS Open the ORCID record for ANTHONY GENEVOIS [Opens in a new window]  and
OLGA VARGHESE Open the ORCID record for OLGA VARGHESE [Opens in a new window]
ANTHONY GENEVOIS*
Affiliation:
Département de Mathématiques, Bâtiment 307, Faculté des Sciences d’Orsay, Université Paris-Sud, F-91405 Orsay, France email anthony.genevois@math.u-psud.fr
OLGA VARGHESE
Affiliation:
Department of Mathematics, Münster University, Einsteinstraße 62, 48149 Münster, Germany email olga.varghese@uni-muenster.de
*
✉anthony.genevois@math.u-psud.fr
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Abstract

An automorphism of a graph product of groups is conjugating if it sends each factor to a conjugate of a factor (possibly different). In this article, we determine precisely when the group of conjugating automorphisms of a graph product satisfies Kazhdan’s property (T) and when it satisfies some vastness properties including SQ-universality.

Keywords

graph product of groupsconjugating automorphismKazhdan’s property (T)SQ-universality

MSC classification

Primary: 20F65: Geometric group theory
Secondary: 05C25: Graphs and abstract algebra (groups, rings, fields, etc.) 20F28: Automorphism groups of groups
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 101 , Issue 2 , April 2020 , pp. 272 - 282
Copyright
© 2019 Australian Mathematical Publishing Association Inc.

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Footnotes

The first author was supported by a public grant as part of the Fondation Mathématique Jacques Hadamard. The second author was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044, Mathematics Münster: Dynamics–Geometry–Structure.

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