AUTOMORPHISM AND OUTER AUTOMORPHISM GROUPS OF RIGHT-ANGLED ARTIN GROUPS ARE NOT RELATIVELY HYPERBOLIC

We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least three vertices are not relatively hyperbolic. We then show that the outer automorphism groups are also not relatively hyperbolic, except for a few exceptional cases. In these cases, the outer automo...

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Bibliographic Details
Published inBulletin of the Australian Mathematical Society Vol. 106; no. 1; pp. 102 - 112
Main Authors KIM, JUNSEOK, OH, SANGROK, TRANCHIDA, PHILIPPE
Format Journal Article
LanguageEnglish
Published Cambridge, UK Cambridge University Press 01.08.2022
Subjects
Apexes
Automorphisms
Group theory
20F65
right-angled Artin group
automorphism group
20F67
relative hyperbolicity
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Summary:We show that the automorphism groups of right-angled Artin groups whose defining graphs have at least three vertices are not relatively hyperbolic. We then show that the outer automorphism groups are also not relatively hyperbolic, except for a few exceptional cases. In these cases, the outer automorphism groups are virtually isomorphic to either a finite group, an infinite cyclic group or $\mathrm {GL}_2(\mathbb {Z})$ .
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972721001258