Related papers: Appendix to Discrete localities II: p-local compac…

We consider random walks on locally compact groups, extending the geometric criteria for the identification of their Poisson boundary previously known for discrete groups. First, we prove a version of the Shannon-McMillan-Breiman theorem,…

We generalize the Cauchy-Davenport theorem to locally compact groups.

Finite non-abelian non-metacyclic $2$-generated $p$-groups (${p>2}$) of nilpotency class $2$ with cyclic commutator subgroup which are the additive groups of local nearrings are described. It is shown that the subgroup of all non-invertible…

We show that a finitely generated group of analytic diffeomorphisms that is expanding and locally discrete in the analytic category is analytically conjugate to a uniform lattice of a finite covering of the group of projective maps of the…

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 use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This…

The aim of this note is to insert in the literature some easy but apparently not widely known facts about morphisms of locally compact groups, all of which are concerned with the openness of the morphism.

In this appendix we provide additional supplementary material to "A Collective, Probabilistic Approach to Schema Mapping." We include an additional extended example, supplementary experiment details, and proof for the complexity result…

In this paper, we define locally matchable subsets of a group which is derived from the concept of matchings in groups and used as a tool to give alternative proofs for existing results in matching theory. We also give the linear analogue…

We describe our online database of finite extensions of the p-adic numbers, and how it can be used to facilitate local analysis of number fields.

We give some new characterizations of exactness for locally compact second countable groups. In particular, we prove that a locally compact second countable group is exact if and only if it admits a topologically amenable action on a…

We survey the recent applications and developments of sieve methods related to discrete groups, especially in the case of infinite index subgroups of arithmetic groups.

In this paper we use families of finite subgroups to study Grothendieck rings associated to certain discrete groups, such as the arithmetic ones.

We study final group topologies and their relations to compactness properties. In particular, we are interested in situations where a colimit or direct limit is locally compact, a k_\omega-space, or locally k_\omega. As a first application,…

Let $p$ be a prime, $P$ a finite p-group and $\cal F$ a Frobenius $P$-category. In "Existence, uniqueness and functoriality of the perfect locality over a Frobenius $P$-category", Algebra Colloquium, 23(2016) 541-622, we also claimed the…

The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…

We introduce the notion of commability between locally compact groups, namely the equivalence relation generated by cocompact inclusions and quotients by compact normal subgroups. We give a classification of focal hyperbolic locally compact…

Solutions of the discrete Painlev\'e II hierarchy are shown to be in relation with a family of Toeplitz determinants describing certain quantities in multicritical random partitions models, for which the limiting behavior has been recently…

In this work we show a compactness Theorem for discrete functions on Poisson point clouds. We consider sequences with equibounded non-local $p$-Dirichlet energy: the novelty consists in the intermediate-interaction regime at which the…

For a locally compact group, property RD gives a control on the convolution norm of any compactly supported measure in terms of the $L^2$-norm of its density and the diameter of its support. We give a complete classification of those Lie…