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A characterization of virtually free groups among hyperbolic groups

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

Published online by Cambridge University Press:  13 January 2025

André Carvalho Open the ORCID record for André Carvalho [Opens in a new window]
André Carvalho*
Affiliation:
Centre of Mathematics, Department of Mathematics, Faculty of Sciences of the University of Porto, Rua do Campo Alegre, s/n, Porto 4169-007, Portugal
*
e-mail: andrecruzcarvalho@gmail.com
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Abstract

We prove that virtually free groups are precisely the hyperbolic groups admitting a language of geodesic words containing a unique representative for each group element with bounded triangles. Equivalently, these are exactly the hyperbolic groups for which the model for the Gromov boundary defined by Silva is well defined.

Keywords

Virtually free groupsGromov boundarygeodesics

MSC classification

Primary: 20E05: Free nonabelian groups 20F67: Hyperbolic groups and nonpositively curved groups
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 7
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

The author was partially supported by CMUP, member of LASI, which is financed by national funds through the FCT – Fundação para a Ciência e a Tecnologia, I.P., under the projects with reference UIDB/00144/2020 and UIDP/00144/2020.

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