Related papers: Locally compact sofic groups
We introduce a new class of locally compact groups, namely the strongly compactly covered groups, which are the Hausdorff topological groups $G$ such that every element of $G$ is contained in a compact open normal subgroup of $G$. For…
We analyze the structure of locally compact groups which can be built up from p-adic Lie groups, for p in a given set of primes. In particular, we calculate the scale function and determine tidy subgroups for such groups, and use them to…
We continue in this paper the study of locally minimal groups started in \cite{LocMin}. The minimality criterion for dense subgroups of compact groups is extended to local minimality. Using this criterion we characterize the compact abelian…
We generalize the concept of stabilizer subgroups to compact quantum groups.
Let $G$ be a locally compact group and $1\leq p<\infty$. Based on some important earlier works, in this paper the concept of $L_p^T-$function is introduced. Then the structure of the space $L^{T}_p(G)$, which is consisting of all…
We give an example of a sofic group, which is not a limit of amenable groups.
This is a survey of some problems in geometric group theory which I find interesting. The problems are from different areas of group theory. Each section is devoted to problems in one area. It contains an introduction where I give some…
We introduce a novel collection of uniqueness problems, with related sampling and interpolation issues. We call them deep zero problems, as they are concerned with local properties at a small number of given points.
The purpose of this paper is to explore the concept of localization, which comes from homotopy theory, in the context of finite simple groups. We give an easy criterion for a finite simple group to be a localization of some simple subgroup…
We introduce and study the class of spherically ordered groups. The notions of spherically ordered groups and their spectra of spherical orderability are introduced. Values of these spectra are found for a series of natural groups.
The aim of this paper is to introduce and give preliminary investigation of T-locally compact spaces. Locally compact and T-locally compact are independent of each other. Every Hausdorff, locally compact space is T-locally compact.…
In this short note we introduce a notion called "quantum injectivity" of locally compact quantum groups, and prove that it is equivalent to amenability of the dual. Particularly, this provides a new characterization of amenability of…
We give a new characterization of partial groups as a subcategory of symmetric (simplicial) sets. This subcategory has an explicit reflection, which permits one to compute colimits in the category of partial groups. We also introduce the…
A locally compact contraction group is a pair (G,f) where G is a locally compact group and f an automorphism of G which is contractive in the sense that the forward orbit under f of each g in G converges to the neutral element e, as n tends…
As a part of our program for Geometric Arithmetic, we develop an arithmetic cohomology theory for number fields using theory of locally compact groups.
We describe the global structure of totally disconnected locally compact groups having a linear open compact subgroup. Among the applications, we show that if a non-discrete, compactly generated, topologically simple, totally disconnected…
In this paper, we study some characterizations of fuzzifying strong compactness including nets and pre-subbases properties. We also introduve new characterizations of locally strong compactness in fuzzifying topology and mappings.
We embed a countably categorical group G into a locally compact group c(G) with a non-trivial topology and study how topological properties of c(G) are connected with the structure of definable subgroups of G.
We present a simple-to-apply criterion for recognizing topological groups that are (locally) homeomorphic to LF-spaces.
This study establishes the variational principle for local pressure in the sofic context.