Adjoining conjugating elements to finite groups
Algorithmic verification of quasi-isometry of some HNN-extensions of Abelian groups.
Almost all one-relator groups with at least three generators are residually finite
We prove that with probability tending to 1, a one-relator group with at least three generators and the relator of length is residually finite, is a virtually residually (finite -)group for all sufficiently large , and is coherent. The proof uses both combinatorial group theory and non-trivial results about Brownian motions.
Amalgamated products and finitely presented groups.
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.
Bass and Serre theory and Nielsen transformations (free and free product case)
Berichtigung zu der Arbeit "Gleichungen in freien Produkten mit Amalgan".
Bounded, separating, incompressible surfaces in knot manifolds.
Closedness of a class of groups under free product.
Cohomology with free coefficients of the fundamental group of a graph of groups.
Combination of convergence groups.
Commensurability of graph products.
Complete growth series and products of groups.
Conjugacy pinched and cyclically pinched one-relator groups.
Here we consider two classes of torsion-free one-relator groups which have proved quite amenable to study-the cyclically pinched one-relator groups and the conjugacy pinched one-relator groups. The former is the class of groups which are free products of free groups with cyclic amalgamations while the latter is the class of HNN extensions of free groups with cyclic associated subgroups. Both are generalizations of surface groups. We compare and contrast results in these classes relative to n-freeness,...
Constructable Solvable Groups.