Related papers: Finiteness properties of profinite groups

We prove that several properties of absolute Galois groups are preserved under a profinite completion.

We consider various metric and analytic notions of finiteness on translation surfaces. The Veech group of a surface is discrete if the surface has finite area or is totally bounded.

We consider profinite groups as 2-sorted first order structures, with a group sort, and a second sort which acts as an index set for a uniformly definable basis of neighbourhoods of the identity. It is shown that if the basis consists of…

We characterize the fundamental group of a locally finite graph G with ends combinatorially, as a group of infinite words. Our characterization gives rise to a canonical embedding of this group in the inverse limit of the (free) fundamental…

A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…

We prove that a group acting geometrically on a thick affine building has property (T). A more general criterion for property (T) is given for groups acting on partite complexes.

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…

It is important to classify covering subgroups of the fundamental group of a topological space using their topological properties in the topologized fundamental group. In this paper, we introduce and study some topologies on the fundamental…

This is a survey of the recent work in algorithmic and asymptotic properties of groups. I discuss Dehn functions of groups, complexity of the word problem, Higman embeddings, and constructions of finitely presented groups with extreme…

We define cofinite graphs and cofinite groupoids in a unified way that extends the notion of cofinite groups introduced by Hartley. The common underlying structure of all these objects is that they are directed graphs endowed with a certain…

We present an overview of the theory of finite groups, with regard to their application as flavour symmetries in particle physics. In a general part, we discuss useful theorems concerning group structure, conjugacy classes, representations…

Separability for groups refers to the question which subsets of a group can be detected in its finite quotients. Classically, separability is studied in terms of which classes have a certain separability property, and this question is…

An $integral$ of a group $G$ is a group $H$ whose commutator subgroup is isomorphic to $G$. This paper continues the investigation on integrals of groups started in the work arXiv:1803.10179. We study: (1) A sufficient condition for a bound…

This paper is a follow-up to our joint paper with I. Agol, P. Storm and K. Whyte "Finiteness of arithmetic hyperbolic reflection groups". The main purpose is to investigate the effective side of the method developed there and its possible…

We give a categorical explanation for many properties of profinite coproducts of profinite groups, which were previously proven on a case-by-case basis. All of these properties take the form "certain functors preserve profinite coproducts".…

We address the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative…

We prove that bounded conciseness is a closed property in the space of marked groups. As a consequence, we reformulate a conjecture of Fern\'andez-Alcober and Shumyatsky [7] about conciseness in the class of residually finite groups.

We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.

A classical theorem of Frucht states that any finite group appears as the automorphism group of a finite graph. In the quantum setting the problem is to understand the structure of the compact quantum groups which can appear as quantum…

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…