Related papers: Absolute profinite rigidity, direct products, and …

There are many results showing the connection and phenomenon between some low-dimensional manifolds with the profinite completions of their fundamental groups. We focus on some Seifert 4-manifolds about the extent of their profinite…

We establish {\em{virtual surjection to pairs}} (VSP) as a general criterion for the finite presentability of subdirect products of groups: if $\Gamma_1,...,\Gamma_n$ are finitely presented and $S<\Gamma_1\times...\times\Gamma_n$ projects…

Let $G$ be a group. The permutability graph of subgroups of $G$, denoted by $\Gamma(G)$, is a graph having all the proper subgroups of $G$ as its vertices, and two subgroups are adjacent in $\Gamma(G)$ if and only if they permute. In this…

The goal of this article is to study results and examples concerning finitely presented covers of finitely generated amenable groups. We collect examples of groups $G$ with the following properties: (i) $G$ is finitely generated, (ii) $G$…

Let $\C$ be a variety of finite groups. We use profinite Bass--Serre theory to show that if $u:H\hookrightarrow G$ is a map of finitely generated residually $\C$ groups such that the induced map $\hat{u}:\hat{H}\rightarrow\hat{G}$ is a…

Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…

This note surveys recent progress toward the profinite rigidity of orientable finite-volume hyperbolic 3-manifolds. Beginning in a brief review of some basic settings of profinite completion and rigidity of general groups, we state the…

We prove that each residually finite Baumslag-Solitar group can be distinguished by its finite quotients from all other residually finite Baumslag-Solitar groups.

We prove that if G is the circle group or a profinite group, then the all of the homotopical information of the category of rational G-spectra is captured by triangulated structure of the rational G-equivariant stable homotopy category.…

We classify finite groups $G$ in $\mathrm{PGL}_{4}(\mathbb{C})$ such that $\mathbb{P}^3$ is $G$-birationally rigid.

In this note we prove the following results: $\bullet$ If a finitely presented group $G$ admits a strongly aperiodic SFT, then $G$ has decidable word problem. More generally, for f.g. groups that are not recursively presented, there exists…

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…

We construct a finitely presented group with property (T) which can not act on on reasonable spaces. Such group is constructed using an generalization of Hall embedding theorem, where property (T) is added at the expense of weakening the…

We contribute some information towards finding a general algorithm for constructing, for a given profinite group, $G$, a compact connected space, $X$, such that the full homeomorphism group, $H(X)$, with the compact-open topology is…

We present a construction that yields infinite families of non-isomorphic semidirect products $N \rtimes F_m$ sharing a specified profinite completion. Within each family, $m \ge 2$ is constant and $N$ is a fixed group. For $m=2$ we can…

By a coprime commutator in a profinite group $G$ we mean any element of the form $[x, y]$, where $x,y\in G$ and $(|x|,|y|)=1$. It is well-known that the subgroup generated by the coprime commutators of $G$ is precisely the pronilpotent…

Classes of algebraic structures that are defined by equational laws are called varieties or equational classes. A variety is finitely generated if it is defined by the laws that hold in some fixed finite algebra. We show that every…

Let $A$ be a commutative ring, and assume every non-trivial ideal of $A$ has finite-index. We show that if ${\rm{SL}}_n(A)$ has bounded elementary generation then every conjugation-invariant norm on it is either discrete or precompact. If…

We completely describe the finitely generated pro-$p$ subgroups of the profinite completion of the fundamental group of an arbitrary $3$-manifold. We also prove a pro-$p$ analogue of the main theorem of Bass--Serre theory for finitely…

We prove that affine Coxeter groups are profinitely rigid.