Related papers: The profinite completion of accessible groups
We prove that the class of closed subgroups of free profinite monoids is precisely the class of projective profinite groups. In particular, the profinite groups associated to minimal symbolic dynamical systems by Almeida are projective. Our…
We construct a finitely generated residually finite group $G$ with the property that every finite index subgroup of $G$ contains a subgroup isomorphic to Promislow's group. Hence $G$ does not have a finite index subgroup with the unique…
A survey of recent results about profinite groups, and results about infinite and finite groups where the theory of profinite groups plays a leading role.
We give an explicit description of the free objects in the quasivariety of adequate semigroups, as sets of labelled directed trees under a natural combinatorial multiplication. The morphisms of the free adequate semigroup onto the free…
A subset S of a group G invariably generates G if G = <s^(g(s)) | s in S> for each choice of g(s) in G, s in S. In this paper we study invariable generation of infinite groups, with emphasis on linear groups. Our main result shows that a…
A profinite group equipped with an expansive endomorphism is equivalent to a one-sided group shift. We show that these groups have a very restricted structure. More precisely, we show that any such group can be decomposed into a finite…
The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem…
We prove for residually finite groups the following long standing conjecture: the number of twisted conjugacy classes of an automorphism of a finitely generated group is equal (if it is finite) to the number of finite dimensional…
A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of allowed actions. We provide criteria for determining when a…
We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…
In this paper, we work on the pro-nilpotent group topology of a free group. First we investigate the closure of the product of finitely many subgroups of a free group in the pro-nilpotent group topology. We present an algorithm for the…
We study the profinite genus of HNN-extensions whose associated subgroups are finite. We give precise formulas for the number of isomorphism classes of HNN(G,H,K,t,f) and of its profinite completion and compute the profinite genus of such…
Let C be a class of groups. We give sufficient conditions ensuring that a free product of residually C groups is again residually C, and analogous conditions are given for locally embeddable into C groups. As a corollary, we obtain that the…
We introduce an extension of the (tame) polynomial automorphism group over finite fields: the profinite (tame) polynomial automorphism group, which is obtained by putting a natural topology on the automorphism group. We show that most known…
We construct an infinite finitely generated recursively presented residually finite algorithmically finite group $G$ answering thereby a question of Myasnikov and Osin. Moreover, $G$ is "very infinite" and "very algorithmically finite" in…
We extend the theory of countably generated Demushkin groups to Demushkin groups of arbitrary rank. We investigate their algebraic properties and invariants, count their isomorphism classes and study their realization as absolute Galois…
Henry Wilton classified when a prime three-manifold $M$ has a residually free fundamental group $\pi_1 M$. We prove that the groups $\pi_1 M\times \mathbb Z^n$ are profinitely rigid within finitely generated residually free groups. We also…
Subgroups of direct products of finitely many finitely generated free groups form a natural class that plays an important role in geometric group theory. Its members include fundamental examples, such as the Stallings-Bieri groups. This…
Suppose a group $G$ is quasi-isometric to a free product of a finite set $S$ of finitely generated abelian groups; let $S'$ denote the set of ranks of the free abelian parts of the groups in $S$. Then $G$ is commensurable with the free…
We prove that amongst the class of free-by-cyclic groups, Gromov hyperbolicity is an invariant of the profinite completion. We show that whenever $G$ is a free-by-cyclic group with first Betti number equal to one, and $H$ is a…