Work

On abstract commensurators of groups

Year: 2010

Type: article

Abstract: We prove, under a technical assumption, that the abstract commensurator of a group that splits over a cyclic subgroup is not finitely generated. This applies in particular to free groups, surface groups, and more generally to all torsion-free word-hyperbolic groups with infinite outer automorphism group and abelianization of rank at least 2. On the other hand, we remark that the condition on the outer automorphism group cannot be removed.

Source: Journal of Group Theory

DOI: 10.1515/jgt.2010.021

Authors: L. Bartholdi, O. Bogopolski

Institutions: University of Göttingen, Siberian Branch of the Russian Academy of Sciences, Heinrich Heine University Düsseldorf

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2951781514

FWCI: 0.395

Cites: 8

Cited by: 11

Related to: 10