Related papers: Limit groups, positive-genus towers and measure eq…

If $G$ is a centreless group, then $\tau(G)$ denotes the height of the automorphism tower of $G$. We prove that it is consistent that for every cardinal $\lambda$ and every ordinal $\alpha < \lambda$, there exists a centreless group $G$…

For any prime number p and any positive real number {\alpha}, we construct a finitely generated group {\Gamma} with p-gradient equal to {\alpha}. This construction is used to show that there exist uncountably many pairwise non-commensurable…

If G is a finitely generated powerful pro-p group satisfying a certain law v=1, and if G can be generated by a normal subset T of finite width which satisfies a positive law, we prove that G is nilpotent. Furthermore, the nilpotency class…

Measure free factors are a generalization of the notion of free factors of a group, in a measure theoretic context. We find new families of cyclic measure free factors of free groups and some virtually free groups, following a question by…

We show that all residually finite generalized Baumslag-Solitar groups of rank $n \geq 1$, defined on a finite and connected graph, are self-similar. Furthermore we prove that all residually finite fundamental groups of (finite, connected)…

We study to what extent torsion-free (Gromov)-hyperbolic groups are elementarily equivalent to their finite index subgroups. In particular, we prove that a hyperbolic limit group either is a free product of cyclic groups and surface groups,…

In this article we give a classification of the binary, simple, $\omega$-categorical structures with SU-rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that…

We show that countable non-abelian free groups admit uncountably many mutually singular elementwise conservative non-singular random subgroups, which are supported on infinite subgroups of infinite index and singular with respect to every…

In this paper we prove that a free nilpotent group of finite rank is transitive self-similar. In contrast, we prove that a free metabelian group of rank $r \geq 2$ is not transitive self-similar.

The equivalence (or weak equivalence) classes of orientation-preserving free actions of a finite group G on an orientable 3-dimensional handlebody of genus g can be enumerated in terms of sets of generators of G. They correspond to the…

We study free topological groups defined over uniform spaces in some subclasses of the class NA of non-archimedean groups. Our descriptions of the corresponding topologies show that for metrizable uniformities the corresponding free…

We introduce a class of spaces, called real cubings, and study the stucture of groups acting nicely on these spaces. Just as cubings are a natural generalisation of simplicial trees, real cubings can be regarded as a natural generalisation…

In [FGRS1,FGRS2] the relationship between the universal and elementary theory of a group ring $R[G]$ and the corresponding universal and elementary theory of the associated group $G$ and ring $R$ was examined. Here we assume that $R$ is a…

Given an arbitrary group $G$ we construct a semigroup of idempotents (band) $B_G$ with the property that the free idempotent generated semigroup over $B_G$ has a maximal subgroup isomorphic to $G$. If $G$ is finitely presented then $B_G$ is…

A group $G$ is said to be periodic if for any $g\in G$ there exists a positive integer $n$ with $g^n=id$. We prove that a finitely generated periodic group of homeomorphisms on the 2-torus that preserves a measure $\mu$ is finite. Moreover…

We consider a tower of function fields F_0 < F_1 < ... over a finite field such that every place of every F_i ramified in the tower and the sequence genus(F_i)/[F_i:F_0] has a finite limit. We also construct a tower in which every place…

We show that if a countable group $G$ is the free product of infinite abelian groups, then for every free, probability-measure-preserving (p.m.p.) action of $G$, its orbit equivalence class is weakly dense in the space of p.m.p. actions of…

In this version small mistakes are corrected and the exposition is changed as suggested by the referee (to appear in Canadian Journal of Mathematics). The first main result of the paper is a criterion for a partially commutative group $\GG$…

We offer a criterion for showing that the automorphism group of an ultrahomogeneous structure is topologically 2-generated and even has a cyclically dense conjugacy class. We then show how finite topological rank of the automorphism group…

We investigate products of sets of reals with combinatorial covering properties. A topological space satisfies $\mathsf{S}_1(\Gamma,\Gamma)$ if for each sequence of point-cofinite open covers of the space, one can pick one element from each…