Related papers: Groupes profinis presqu'amalgam\'es

This paper deals with graph automaton groups associated with trees and some generalizations. We start by showing some algebraic properties of tree automaton groups. Then we characterize the associated semigroup, proving that it is…

Let $\Lambda_0$ be an ordered abelian group. We show how an $\mathrm{ATF}(\mathbb{Z}\times\Lambda_0)$ group -- that is, a group admitting a free affine action without inversions on a $\mathbb{Z}\times\Lambda_0$-tree -- admits a natural…

We use the theory of group actions on profinite trees to prove that the fundamental group of a finite, 1-acylindrical graph of free groups with finitely generated edge groups is conjugacy separable. This has several applications: we prove…

We construct the first example of a finitely generated group which has Serre's property (FA) (i.e., whenever it acts on a simplicial tree it fixes a vertex), but admits a fixed point-free action on an $\mathbb{R}$-tree with finite arc…

Let $(\mathcal{G},\Gamma)$ be an abstract graph of finite groups. If $\Gamma$ is finite, we can construct a profinite graph of groups in a natural way $(\hat{\mathcal{G}},\Gamma)$, where $\hat{\mathcal{G}}(m)$ is the profinite completion of…

We introduce the notion of corestricted free products of a family of profinite groups indexed over an arbitrary profinite space. Using arithmetic results of the second author, this enables us to prove an analogue of Riemann's existence…

We investigate fixed subgroups of automorphisms of generalised Baumslag-Solitar (GBS) groups. Our main results are for automorphisms leaving a Bass-Serre tree invariant, under the assumption that all edge stabilisers are strictly contained…

To a large class of graphs of groups we associate a C*-algebra universal for generators and relations. We show that this C*-algebra is stably isomorphic to the crossed product induced from the action of the fundamental group of the graph of…

We study the subgroup structure of the \'etale fundamental group $\Pi$ of a projective curve over an algebraically closed field of characteristic 0. We obtain an analog of the diamond theorem for $\Pi$. As a consequence we show that most…

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…

We give a simple proof of the finite presentation of Sela's limit groups by using free actions on $\bbR^n$-trees. We first prove that Sela's limit groups do have a free action on an $\bbR^n$-tree. We then prove that a finitely generated…

Let $\Pi$ be the \'etale fundamental group of a smooth affine curve over an algebraically closed field of characteristic $p>0$. We establish a criterion for profinite freeness of closed subgroups of $\Pi$. Roughly speaking, if a closed…

Profinite semigroups are a generalization of finite semigroups that come about naturally when one is interested in considering free structures with respect to classes of finite semigroups. They also appear naturally through dualization of…

We show that for groups acting acylindrically on simplicial trees the $K$- and $L$-theoretic Farrell-Jones Conjecture relative to the family of subgroups consisting of virtually cyclic subgroups and all subconjugates of vertex stabilisers…

The main result of this paper is the following theorem. Let q be a prime, A an elementary abelian group of order q^3. Suppose that A acts as a coprime group of automorphisms on a profinite group G in such a manner that C_G(a)' is periodic…

Let $\mathfrak C$ be a class of finite groups which is closed for subgroups, quotients and direct products. Given a profinite group $G$ and an element $x\in G$, we denote by $P_{\mathfrak{C}}(x,G)$ the probability that $x$ and a randomly…

First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an…

We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties take the form "certain functors preserve profinite coproducts".…

Compact connected abelian groups, or protori, have intrinsic structural characteristics that present for the entire category. In the case of finite-dimensional torus-free protori, The Resolution Theorem for Compact Abelian Groups sets the…

Finitely generated (non-abelian) free metabelian pro-p groups, and wreath products of f.g. free abelian pro-p groups, are all finitely axiomatizable in the class of all profinite groups.