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Accessible Unlicensed Requires Authentication Published by De Gruyter April 23, 2010

On abstract commensurators of groups

L. Bartholdi and O. Bogopolski
From the journal


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.

Received: 2009-09-25
Revised: 2009-11-11
Published Online: 2010-04-23
Published in Print: 2010-November

© de Gruyter 2010