Related papers: Order separability

This is an introduction to some of the most probabilistic aspects of free probability theory.

This is the third article in a series of four articles dealing with the P vs. NP question. The purpose of this work is to demonstrate that the methods used in the first two articles of this series are not affected by oracle relativizations.…

For a subgroup of a free product of finite groups, we obtain necessary conditions (on its Kurosh decomposition) to be verbally closed.

In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.

One of the better studied properties for operators in judgment aggregation is independence, which essentially dictates that the collective judgment on one issue should not depend on the individual judgments given on some other issue(s) in…

Let $G$ be a finite group of order $n$, and denote by $\rho(G)$ the product of element orders of $G$. The aim of this work is to provide some upper bounds for $\rho(G)$ depending only on $n$ and on its least prime divisor, when $G$ belongs…

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 give a detailed analysis of the proportion of elements in the symmetric group on $n$ points whose order divides $m$, for $n$ sufficiently large and $m \ge n$ with $m = O(n)$.

We investigate when the independence complex of $G[H]$, the lexicographical product of two graphs $G$ and $H$, is either vertex decomposable or shellable. As an application, we construct an infinite family of graphs with the property that…

This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems,…

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 definition of free product of operads, following the definition of a free product of algebras. There is a given method of finding the basis and dimension of the free product of operads. By anti-commutative…

In this paper, we summarize the work on the characterization of finite simple groups and the study on finite groups with the set of element orders and two orders (the order of group and the set of element orders). Some related topics, and…

The purpose of this paper is to study the transitive group-groupoids.

We define and study a notion of free wreath product with amalgamation for compact quantum groups. These objects were already introduced in the case of duals of discrete groups under the name "free wreath products of pairs" in a previous…

We extend the classical construction by Noether of crossed product algebras, defined by finite Galois field extensions, to cover the case of separable (but not necessarily finite or normal) field extensions. This leads us naturally to…

The far-reaching work of Dahmani-Guirardel-Osin and recent work of Clay-Mangahas-Margalit provide geometric approaches to the study of the normal closure of a subgroup (or a collection of subgroups)in an ambient group $G$. Their work gives…

We present a criterion of separability for arbitrary s partitions of N-particle fermionic pure states. We show that, despite the superficial non-factorizability due to the antisymmetry required by the indistinguishability of the particles,…

We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only "quantifier elimination relative to ordered sets" in the following sense. Each definable set in…

Notions of freedom and independence for hypergraphs of models of a theory are defined. Properties of these notions and their applications to some natural classes of theories are studied.