Commensurations and metric properties of houghton’s groups
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Burillo, José; Cleary, Sean; Martino, Armando; Röver, Claas (2016). Commensurations and metric properties of houghton’s groups. Pacific Journal of Mathematics 285 (2), 289-301
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.