Amalgams of torsion-free nilpotent groups of class three
Amenable actions of amalgamated free products of free groups over a cyclic subgroup and generic property
We show that the amalgamated free products of two free groups over a cyclic subgroup admit amenable, faithful and transitive actions on infinite countable sets. This work generalizes the results on such actions for doubles of free group on two generators.
Amenable, transitive and faithful actions of groups acting on trees
We study under which condition an amalgamated free product or an HNN-extension over a finite subgroup admits an amenable, transitive and faithful action on an infinite countable set. We show that such an action exists if the initial groups admit an amenable and almost free action with infinite orbits (e.g. virtually free groups or infinite amenable groups). Our result relies on the Baire category Theorem. We extend the result to groups acting on trees.
An algorithm for the word problem in extensions and the dependence of its complexity on the group representation
Anwendungen der Nielsenschen Kürzungsmethode in Gruppen mit einer definierenden Relation.
Aspherical Group Presentations.