Related papers: An (FA)-group that is not (FR)

We prove that the abstract commensurator of a nonabelian free group, an infinite surface group, or more generally of a group that splits appropriately over a cyclic subgroup, is not finitely generated. This applies in particular to all…

We prove that a finitely generated group contains a sequence of non-trivial elements which converge to the identity in every compact homomorphic image if and only if the group is not virtually abelian.

We show that if a group $G$ acting faithfully on a rooted tree $T$ has a free subgroup, then either there exists a point $w$ of the boundary $\partial T$ and a free subgroup of $G$ with trivial stabilizer of $w$, or there exists…

We study non-nesting actions of groups on real trees. We prove some fixed point theorems for such actions under the assumption that groups are Polish and have comeagre conjugacy classes.

We provide examples of finite non-abelian groups acting on non-trivial Severi-Brauer surfaces.

Let $k$ be a finitely generated field, let $X$ be an algebraic variety and $G$ a linear algebraic group, both defined over $k$. Suppose $G$ acts on $X$ and every element of a Zariski-dense semigroup $\Gamma \subset G(k)$ has a rational…

The phase structure of the scalar field theory with arbitrary powers of the gradient operator and a local non-analytic potential is investigated by the help of the RG in Euclidean space. The RG equation for the generating function of the…

Kurz et al. have recently shown that infinite $\lambda$-trees with finitely many free variables modulo $\alpha$-equivalence form a final coalgebra for a functor on the category of nominal sets. Here we investigate the rational fixpoint of…

We give two examples of a finitely generated subgroup of a free group and a subset, closed in the profinite topology of a free group, such that their product is not closed in the profinite topology of a free group.

We consider the action of $p$-toral subgroups of $U(n)$ on the unitary partition complex $\mathcal L_n$. We show that if $H\subseteq U(n)$ is $p$-toral and has noncontractible fixed points on $\mathcal L_n$, then the image of $H$ in the…

We demonstrate the existence of a family of finitely generated subgroups of Richard Thompson's group $F$ which is strictly well-ordered by the embeddability relation in type $\epsilon_0 +1$. All except the maximum element of this family…

We prove that thick groups (and more generally thick graphs) have trivial Floyd boundary. This shows a wide class of finitely generated groups that are non-relatively hyperbolic have trivial Floyd boundary. In addition to giving new…

We identify natural conditions for a countable group acting on a countable tree which imply that the orbit equivalence relation of the induced action on the Gromov boundary is Borel hyperfinite. Examples of this condition include…

We construct uncountably many discrete groups of type $FP$; in particular we construct groups of type $FP$ that do not embed in any finitely presented group. We compute the ordinary, $\ell^2$- and compactly-supported cohomology of these…

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

A concrete family of automorphisms alpha_n of the free group F_n is exhibited, for any n > 2, and the following properties are proved: alpha_n is irreducible with irreducible powers, has trivial fixed subgroup, and has 2n-1 attractive as…

If G is a group, a pseudocharacter f: G-->R is a function which is "almost" a homomorphism. If G admits a nontrivial pseudocharacter f, we define the space of ends of G relative to f and show that if the space of ends is complicated enough,…

Let $G$ be a finitely generated group acting faithfully and properly discontinuously by homeomorphisms on a planar surface $X \subseteq \mathbb{S}^2$. We prove that $G$ admits such an action that is in addition co-compact, provided we can…

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…

For any countable group with infinite conjugacy classes we construct a family of forests on the group. For each of them there is a random walk on the group with the property that its sample paths almost surely converge to the geometric…