Related papers: Random triangular Burnside groups
We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…
We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those…
It is conjectured that the central quotient of every irreducible Artin group is either virtually cyclic or acylindrically hyperbolic. We prove this conjecture for Artin groups associated to triangle-free graphs and Artin groups of large…
We introduce a construction that simultaneously yields cusped spaces of relatively hyperbolic groups, and spaces quasi-isometric to Teichmueller metrics. We use this to study Dehn-filling-like quotients of various groups, among which…
An open question asks whether every group acting acylindrically on a hyperbolic space has uniform exponential growth. We prove that the class of groups of uniform uniform exponential growth acting acylindrically on a hyperbolic space is…
We provide new computations in bounded cohomology: A group is boundedly acyclic if its bounded cohomology with trivial real coefficients is zero in all positive degrees. We show that there exists a continuum of finitely generated…
In this paper we study the hyperbolicity properties of a class of random groups arising as graph products associated to random graphs. Recall, that the construction of a graph product is a generalization of the constructions of right-angled…
We prove that there exist finitely presented, residually finite groups that are profinitely rigid in the class of all finitely presented groups but not in the class of all finitely generated groups. These groups are of the form $\Gamma…
After we have given a survey on the Burnside ring of a finite group, we discuss and analyze various extensions of this notion to infinite (discrete) groups. The first three are the finite-G-set-version, the inverse-limit-version and the…
We construct the first examples of an algorithmically complex finitely presented residually finite groups and first examples of finitely presented residually finite groups with arbitrarily large (recursive) Dehn function and depth function.…
We consider certain finite sets of circle-valued functions defined on intervals of real numbers and estimate how large the intervals must be for the values of these functions to be uniformly distributed in an approximate way. This is used…
We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small cancellation conditions. Using…
We study infinitesimal generators of one-parameter semigroups in the unit disk $\mathbb D$ having prescribed boundary regular fixed points. Using an explicit representation of such infinitesimal generators in combination with Krein-Milman…
In this article we aim to develop from first principles a theory of sum sets and partial sum sets, which are defined analogously to difference sets and partial difference sets. We obtain non-existence results and characterisations. In…
We define and study the class of inner ultrahomogeneous groups, which includes Hall's universal group and the universal locally recursively presentable group. We provide simple criteria for ample generic automorphisms, straight maximality,…
We prove that if $\pi$ is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are $\pi$-groups. In particular, when $\pi$ is the empty set, we obtain Henckell's decidability of…
Given a finitely generated group $G$ that is relatively finitely presented with respect to a collection of peripheral subgroups, we prove that every infinite subgroup $H$ of $G$ that is bounded in the relative Cayley graph of $G$ is…
The density conjecture of Bers, Sullivan and Thurston predicts that each complete hyperbolic 3-manifold M with finitely generated fundamental group is an algebraic limit of geometrically finite hyperbolic 3-manifolds. We prove that the…
We give continued fraction algorithms for a particular class of Fuchsian triangle groups. In particular, we give an explicit form of each such group that is a subgroup of the Hilbert modular group of its trace field and provide an interval…
In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural…