Related papers: Property FA is not a profinite property

It is proved that every finitely generated profinite group with fewer than $2^{\aleph_0}$ conjugacy classes of elements of infinite order is finite

It is shown that for any action of a finitely presented group $G$ on an $\R$-tree, there is a decomposition of $G$ as the fundamental group of a graph of groups related to this action. If the action of $G$ on $T$ is non-trivial, i.e. there…

In this paper, we study groups with property (PPH), i.e., there exist finitely many proper Gromov-hyperbolic spaces $X_1,\ldots, X_l$ on which $G$ acts cocompactly such that the diagonal action of $G$ on the $\ell^1$-product…

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…

This is an addendum to arXiv: 0810.5376. We show, using our methods and an auxiliary result of Bestvina-Bromberg-Fujiwara, that a finitely generated group with infinitely many pairwise non-conjugate homomorphisms to a mapping class group…

The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…

For profinite branch groups, we first demonstrate the equivalence of the Bergman property, uncountable cofinality, Cayley boundedness, the countable index property, and the condition that every non-trivial normal subgroup is open; compact…

We prove that for every prime $p$ algebraically clean graphs of groups are virtually residually $p$-finite and cohomologically $p$-complete. We also prove that they are cohomologically good. We apply this to certain $2$-dimensional Artin…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

We prove a number of results about profinite completions of Coxeter groups. For example we prove Coxeter groups are good in the sense of Serre and that various splittings of Coxeter groups arising from actions on trees are detected by the…

The group property FW stands in-between the celebrated Kazdhan's property (T) and Serre's property FA. Among many characterizations, it might be defined, for finitely generated groups, as having all Schreier graphs one-ended. It follows…

From many supercompact cardinals, we show that it is consistent for the tree property to hold at many small successors of singular cardinals, each with a different cofinality. In particular, we construct a model in which the tree property…

We introduce a new iterative amalgamated free product construction of II$_1$ factors, and use it to construct a separable II$_1$ factor which does not have property Gamma and is not elementarily equivalent to the free group factor…

We define for discrete finitely presented groups a new property related to their asymptotic representations. Namely we say that a groups has the property AGA if every almost representation generates an asymptotic representation. We give…

We present novel constructions concerning the homology of finitely generated groups. Each construction draws on ideas of Gilbert Baumslag. There is a finitely presented acyclic group $U$ such that $U$ has no proper subgroups of finite index…

We undertake the study of profinite quandles. We provide several constructions of profinite quandles from profinite groups, and from other profinite quandle. We characterize which subquandles of profinite quandles are again profinite.…

Let $K$ be a global function field of characteristic $p$, and let $\Gamma$ be a finite-index subgroup of an arithmetic group defined with respect to $K$ and such that any torsion element of $\Gamma$ is a $p$-torsion element. We define…

Automatic presentations, also called FA-presentations, were introduced to extend finite model theory to infinite structures whilst retaining the solubility of fundamental decision problems. This paper studies FA-presentable algebras. First,…

Let $A$ be an abelian variety defined over a field $K.$ We study finite generation properties of the profinite group $\mathrm{Gal}(\Omega/K)$ and of certain closed normal subgroups thereof, where $\Omega$ is the torsion field of $A$ over…

Relational semigroups with domain and range are a useful tool for modelling nondeterministic programs. We prove that the representation class of domain-range semigroups with demonic composition is not finitely axiomatisable. We extend the…