In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Also, we show that right-angled Artin groups are conjugacy separable. Moreover, we investigate the profinite topology of F 2 × F 2 and of the group L in [22], which are the only obstructions for the subgroup separability of th...

In the present work, we give necessary and sufficient conditions on the graph of a right-angled Artin group that determine whether the group is subgroup separable or not. Also, we show that right-angled Artin groups are conjugacy separable. Moreover, we investigate the profinite topology of F 2 × F 2 and of the group L in [22], which are the only obstructions for the subgroup separability of th...

A directed set I is a partially ordered set such that for all i, j ∈ I there exists a k ∈ I such that k ≥ i and k ≥ j. An inverse system of groups is a collection of groups {Gi} indexed by a directed set I together with group homomorphisms πij : Gi −→ Gj whenever i ≥ j such that πii = idGi and πjk ◦ πij = πik. Let H be a group. We call a family of homomorphisms {ψi : H −→ Gi : i ∈ I} compatible...

Some fundamental questions about infinite-vertex (free) profinite semigroupoids are clarified, putting in evidence differences with the finitevertex case. This is done with examples of free profinite semigroupoids generated by the graph of a subshift. It is also proved that for minimal subshifts, the infinite edges of such free profinite semigroupoids form a connected compact groupoid.

we analyze some properties of the distribution $q_{g,k}$ of the first component in a $k$-tuple chosen uniformly‎ ‎in the set of all the $k$-tuples generating a finite group $g$ (the limiting distribution of the product replacement algorithm)‎. ‎in particular‎, ‎we concentrate our attention on‎ ‎the study of the variation distance $beta_k(g)$ between $q_{g,k}$ and the uniform distribution‎. ‎we ...

LET G be a residually-finite torsion-free group. Is Gthe profinite completion of G-torsion free? This question was asked in [CKL] where it was shown that if G is a finitely generated metabelian-by-finite group then indeed G is torsion free. On the other hand Evans [E] showed that if G is not finitely generated then it is possible that G has torsion. His example is also metabelian. In this note ...