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Commensurations and
metric properties of Houghton's groups
José Burillo, Sean Cleary, Armando Martino and Claas E. Röver |
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Vol. 285 (2016), No. 2, 289–301
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Abstract |
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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. |
Keywords
Houghton's groups, commensurations
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Mathematical Subject Classification 2010
Primary: 20F65
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Milestones
Received: 22 February 2016
Accepted: 18 May 2016
Published: 21 November 2016
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Authors |
| José Burillo | |
| Departament de Matemàtica Aplicada
IV EETAC-UPC Esteve Terrades 5 08860 Castelldefels Spain |
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| Sean Cleary | |
| Department of Mathematics
R8133 The City College of New York 160 Convent Avenue New York, NY 10031 United States |
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| Armando Martino | |
| Mathematical Sciences University of Southampton University Road Southampton SO17 1BJ United Kingdom |
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| Claas E. Röver | |
| School of Mathematics, Statistics
and Applied Mathematics NUI Galway University Road Galway Ireland |
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