Commensurations and metric properties of Houghton's groups

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To access the full text documents, please follow this link: http://hdl.handle.net/2117/103242

Title:	Commensurations and metric properties of Houghton's groups
Author:	Burillo Puig, José; Cleary, Sean; Martino, Armando; Röver, Claas E.
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. COMBGRAPH - Combinatòria, Teoria de Grafs i Aplicacions
Abstract:	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.
Abstract:	Peer Reviewed
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra::Teoria de grups -Àrees temàtiques de la UPC::Matemàtiques i estadística::Geometria::Geometria algebraica -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
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Document type:	Article - Submitted version Article
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