Related papers: What Is... A Thin Group?
The paper begins by exploring the various definitions of norms on semigroups and then presents a new definition of a normed semigroup. The properties of normed semigroups in the new sense are investigated. The new definition of the norm is…
This book is an introduction to a fast developing branch of mathematics - the theory of representations of groups. It presents classical results of this theory concerning finite groups.
This text is an introduction to the study of NIP (or dependent) theories. It is meant to serve two purposes. The first is to present various aspects of NIP theories and give the reader the background material needed to understand almost any…
This is a very brief introduction to Wilson's Renormalization Group with emphasis on mathematical developments.
The aim of this text is to provide a clear description of the theory of Infra-nilmanifolds and their fundamental groups, the almost-Bieberbach groups. For most of the proofs of the results, we refer to the literature. Nevertheless, at…
We study thick subcategories defined by modules of complexity one in $\underline{\md}R$, where $R$ is the exterior algebra in $n+1$ indeterminates.
This is an informal announcement of results to be described and proved in detail in a paper to appear. We give various results on the structure of approximate subgroups in linear groups such as $\SL_n(k)$. For example, generalising a result…
A subgroup $H$ of a finite group $G$ is said to be an $\mathscr{H}C$-subgroup of $G$ if there exists a normal subgroup $T$ of $G$ such that $G=HT$ and $H^g \cap N_T(H)\leq H$ for all $g\in G$. In this paper, we investigate the structure of…
Many people have proposed definitions of `weak n-category'. Ten of them are presented here. Each definition is given in two pages, with a further two pages on what happens when n = 0, 1, or 2. The definitions can be read independently.…
The aim of this paper is to present the main constructions of the substructures of an almost groupoid and to discuss their basic properties. The definitions and properties concerning these new algebraic constructions extend to almost…
These notes were prepared for the MSRI hot topics workshop on superstrong approximation (2012). We give a brief overview of the developments in the theory, especially the fundamental expansion theorem. Applications to diophantine problems…
The main purpose of this paper is to give a new definition for the notion of group-groupoid. Also, several basic properties of group-groupoids are established.
In this paper, we introduce the weakly nilpotent hypergroups with giving some new properties, and then establish several structural characterizations of these hypergroups. Some results obtained in this paper answer the two questions raised…
The main goal of this note is to determine and to count the normal subgroups of a ZM-group. We also indicate some necessary and sufficient conditions such that the normal subgroups of a ZM-group form a chain.
This paper gives an introduction to some results on monodromy groupoids and the monodromy principle, and then develops the notion of monodromy groupoid for group groupoids.
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…
In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.
The aim of this manuscript is to give some basic notions related to numerical semigroups, and from these on the one hand describe a classical application to the study of singularities of plane algebraic curves, and on the other, show how…
The purpose of this paper is to study the transitive group-groupoids.
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B contained in A which is embedded with a stronger structure S. These types of structures occurin our…