Related papers: A brief introduction to approximate groups

Given an arbitrary long but finite sequence of observations from a finite set, we construct a simple process that approximates the sequence, in the sense that with high probability the empirical frequency, as well as the empirical one-step…

Approximate group analysis technique, that is, the technique combining the methodology of group analysis and theory of small perturbations, is applied to finite-difference equations approximating ordinary differential equations.…

This is a survey of several exciting recent results in which techniques originating in the area known as additive combinatorics have been applied to give results in other areas, such as group theory, number theory and theoretical computer…

We provide a mathematically rigorous definition of local approximation and demonstrate its applicability to some interesting classes of structures. In particular, we prove that any compact simple Lie group is locally approximated by finite…

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…

ECM survey article discussing the structure of subsets of Abelian groups which behave `a bit like' cosets (of subgroups).

We discuss a selection of recent developments in arithmetic combinatorics having to do with ``approximate algebraic structure'' together with some of their applications.

This is a short survey of amenable equivalence relations.

A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.

Various uses of the renormalization group are examined.

We characterize groups with Guoliang Yu's property A (i.e., exact groups) by the existence of a family of uniformly bounded representations which approximate the trivial representation.

We announce an atlas of subgroup lattices of almost simple groups and present two algorithms that were used to produce the atlas.

This paper aims to examine the version of the topological group structure in proximity and especially descriptive proximity spaces, that is, the concepts of proximal group and descriptive proximal group are introduced. In addition, the…

This is an account of the theory of inverse semigroups, assuming only that the reader knows the basics of semigroup theory.

We study how well a real number can be approximated by sums of two or more rational numbers with denominators up to a certain size.

Quasigroup equational definitions are given.

Approximation theory is concerned with the ability to approximate functions by simpler and more easily calculated functions. The first question we ask in approximation theory concerns the {\it possibility of approximation}. Is the given…

We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated inaccessible pro-$p$…

In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of…

In this paper, we present the concept of Approximate grammar and how it can be used to extract information from a documemt. As the structure of informational strings cannot be defined well in a document, we cannot use the conventional…