Related papers: Cartesian products as profinite completions

We prove that a variety of algebras whose finitely generated members are free must be definitionally equivalent to the variety of sets, the variety of pointed sets, a variety of vector spaces over a division ring, or a variety of affine…

Infinite products, indexed by countably infinite linear orders, arise naturally in the context of fundamental groupoids. Such products are called "transfinite" if the index orders are permitted to contain a dense suborder and are called…

We prove the finite generation of canonical rings of projective variety of general type defined over complex numbers.

Let $\mathcal{C}$ be a class of finite groups closed for subgroups, quotients groups and extensions. Let $\Gamma$ be a finite simplicial graph and $G = G_{\Gamma}$ be the corresponding pro-$\mathcal C$ RAAG. We show that if $N$ is a…

We prove that every finite direct product of crystallographic groups arising from an irreducible root system (in the sense of Lie theory) is profinitely rigid (equiv. first-order rigid). This is a generalization of recent proofs of…

We consider the finite generation property for cohomology algebra of pointed finite tensor categories via de-equivariantization and exact sequence of finite tensor categories. As a result, we prove that all coradically graded pointed finite…

We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

We prove that the crossed product AxG of a unital finitely generated MF algebra A by a discrete finitely generated amenable residually finite group G is an MF algebra, provided that the action is almost periodic. This generalizes a result…

Among all affine, flat, finitely presented group schemes, we focus on those that are pure, this includes all groups which are extensions of a finite locally free group by a group with connected fibres. We prove that over an arbitrary base…

We show that if a group can be represented as a graph product of finite directly indecomposable groups, then this representation is unique.

Let $\mathcal G$ denote the space of finitely generated marked groups. For any finitely generated group $G$, we construct a continuous, injective map $f$ from the space of subgroups $Sub(G)$ to $\mathcal G$ that sends conjugate subgroups to…

Using quantum representations of mapping class groups we prove that profinite completions of Burnside-type surface group quotients are not virtually prosolvable, in general. Further, we construct infinitely many finite simple characteristic…

We define and study the class of positively finitely related (PFR) profinite groups. Positive finite relatedness is a probabilistic property of profinite groups which provides a first step to defining higher finiteness properties of…

We settle an old conjecture of Karrass and Solitar by proving that a finitely generated subgroup of a non-trivial free product $G = A\ast B$ has finite index if and only if it intersects non-trivially each non-trivial normal subgroup of…

We show that up to commensurability there are only finitely many cocompact arithmetic Kleinian groups generated by rotations. This implies, in particular, that there exist only finitely many conjugacy classes of cocompact two generated…

We show that finite (i.e. locally finite and decomposition-finite) objects of a connected Grothendieck topos span a Boolean pretopos with an essentially unique Galois point. The automorphism group of this point carries a profinite topology…

We prove that every finitely generated, residually finite group $G$ embeds into a finitely generated perfect branch group $\Gamma$ such that many properties of $G$ are preserved under this embedding. Among those are the properties of being…

We obtain a complete classification of graph products of finite abelian groups whose Cayley graphs with respect to the standard presentations are planar.

A finitely generated solvable group with unbounded iterated identity is constructed.

This paper establishes strong profinite rigidity results for K\"ahler groups, showing that certain groups are determined within the class of residually finite K\"ahler groups by their profinite completion. Examples include products of…