Commensurations and Metric Properties of Houghton's Groups

José Burillo, Sean Cleary, Armando Martino and Claas Röver

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.

The preprint is available as dvi (38k) or PDF (281k) files, or from the arXiv:1403.0026.

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