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arXiv · 0902.4542

On abstract commensurators of groups

Laurent Bartholdi·Oleg Bogopolski
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Abstract

We prove that the abstract commensurator of a nonabelian free group, an infinite surface group, or more generally of a group that splits appropriately over a cyclic subgroup, is not finitely generated. This applies in particular to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. We also construct a finitely generated, torsion-free group which can be mapped onto Z and which has a finitely generated commensurator.

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Laurent Bartholdi, Oleg Bogopolski. 2009-02-26. On abstract commensurators of groups. https://doi.org/10.1515/jgt.2010.021

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