On abstract commensurators of groups

Details On abstract commensurators of groups On abstract commensurators of groups

2009-02-26

arxiv.org/abs/0902.4542v1

Mathematics

Group Theory

13 pages, no figure

Scientific paper

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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