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Abstract: We prove that the abstract commensurator of a nonabelian free group, aninfinite surface group, or more generally of a group that splits appropriatelyover a cyclic subgroup, is not finitely generated.This applies in particular to all torsion-free word-hyperbolic groups withinfinite outer automorphism group and abelianization of rank at least 2.We also construct a finitely generated, torsion-free group which can bemapped onto Z and which has a finitely generated commensurator.



Autor: Laurent Bartholdi, Oleg Bogopolski

Fuente: https://arxiv.org/







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