Related papers: On asymptotically free action of permutation group…

In this paper, we show that if a group acts isometrically on a good hyperbolic space of finite volume entropy through a non-elementary action, then it admits an affine action on some $L^p$ -space with an unbounded orbit for sufficiently…

In this article, we consider actions of \mathcal{Z}_+^d, \mathcal{R}_+^d and finitely generated free groups on a von Neumann algebras $M$ and prove a version of maximal ergodic inequality. Additionally, we establish non-commutative…

Given an action of a group G on a topological space X, we establish a necessary and sufficient condition for the existence of a free subgroup F of rank 2 of G acting properly discontinuously on at least one nonempty, open, F-invariant…

We show that given any subgroup F of R_+ which is either countable or belongs to a certain "large" class of uncountable subgroups, there exist continuously many free ergodic probability measure preserving actions \sigma_i of the free group…

An action of a group $G$ on a set $X$ is said to be quasi-n-transitive if the diagonal action of $G$ on $X^n$ has only finitely many orbits. We show that branch groups, a special class of groups of automorphisms of rooted trees, cannot act…

A directed graph is oriented if it can be obtained by orienting the edges of a simple, undirected graph. For an oriented graph $G$, let $\beta(G)$ denote the size of a minimum feedback arc set, a smallest subset of edges whose deletion…

The paper presents conditions on entry permutations that induce asymptotic freeness when acting on Gaussian random matrices. The class of permutations described includes the matrix transpose, as well as entry permutations relevant in…

Let G be a group, and let M=(m_n) be a sequence of finitely supported probability measures on G. Consider the probability that two elements chosen independently according to m_n commute. Antolin, Martino and Ventura define the 'degree of…

Let $G$ be a finite group acting on a vector space $V = \mathbb{F}_p^n$ over a prime field. Given finite sets $S \subset G$ and $E \subset V$, we study the restricted orbit union $S(E) = \bigcup_{g\in S} g(E)$ and establish quantitative…

Let $G$ be a closed permutation group on a countably infinite set $\Omega$, which acts transitively but not highly transitively. If $G$ is oligomorphic, has no algebraicity and weakly eliminates imaginaries, we prove that any probability…

Given a group G, we construct, in a canonical way, an inverse semigroup S(G) associated to G. The actions of S(G) are shown to be in one-to-one correspondence with the partial actions of G, both in the case of actions on a set, and that of…

Let L be a Lie group and Lambda a lattice in L. Suppose G is a non-compact simple Lie group realized as a Lie subgroup of L, and the image of G on L/Lambda is dense. Let c be a diagonalizable element of G not contained in a compact…

We prove constructively that the maximum possible number of minimal connected dominating sets in a connected undirected graph of order $n$ is in $\Omega(1.489^n)$. This improves the previously known lower bound of $\Omega(1.4422^n)$ and…

Let $G$ be the general linear group of the degree $n\geq 2$ over the field $\mathbb{K}=\mathbb{R}$ or $\mathbb{C}$. In this article, we give a description of orbit decomposition of the multiple projective space $G^m/P^m$ under the diagonal…

A graph is edge-transitive if its automorphism group acts transitively on the edge set. In this paper, we investigate the automorphism groups of edge-transitive graphs of odd order and twice prime valency. Let $\Gamma$ be a connected graph…

A graph $G$ is called universal for a family of graphs $\mathcal{F}$ if it contains every element $F \in \mathcal{F}$ as a subgraph. Let $\mathcal{F}(n,2)$ be the family of all graphs with maximum degree $2$. Ferber, Kronenberg, and Luh…

Let $G$ be a graph whose edges are each assigned one of the $m$-colours $1, 2, \ldots, m$, and let $\Gamma$ be a subgroup of $S_m$. The operation of switching at a vertex $x$ with respect $\pi \in \Gamma$ permutes the colours of the edges…

Let $G$ be a nontrivial transitive permutation group on a finite set $\Omega$. An element of $G$ is said to be a derangement if it has no fixed points on $\Omega$. From the orbit counting lemma, it follows that $G$ contains a derangement,…

The paper offers a thorough study of multiorders and their applications to measure-preserving actions of countable amenable groups. By a~{\em multiorder} on a~countable group we mean any probability measure $\nu$ on the collection…

We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. Inspired to the recent paper \cite{gb2}, see also \cite{ch} and \cite{pacini}, we study Lagrangian orbits of…