Commensurations and metric properties of Houghton's groups
We describe the automorphism groups and the abstract commensurators of Houghton’s groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton grou...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2016 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/103242 |
| Acceso en línea: | https://hdl.handle.net/2117/103242 https://dx.doi.org/10.2140/pjm.2016.285.289 |
| Access Level: | acceso abierto |
| Palabra clave: | Group theory Geometry Topology Houghton's groups commensurations Grups, Teoria de Geometria Topologia Classificació AMS::14 Algebraic geometry::14L Algebraic groups Classificació AMS::51 Geometry::51H Topological geometry Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica |
| Sumario: | We describe the automorphism groups and the abstract commensurators of Houghton’s groups. Then we give sharp estimates for the word metric of these groups and deduce that the commensurators embed into the corresponding quasi-isometry groups. As a further consequence, we obtain that the Houghton group on two rays is at least quadratically distorted in those with three or more rays. |
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