Related papers: On certain semigroups of transformations with an i…

In this article, we prove that if all non-trivial cyclic subgroups of a group $G$ are self normalizing and $G$ satisfies the implication $$ \ o(x)\neq o(y)\Rightarrow o(xy)\neq o(x), o(y), $$ for all non-trivial elements $x$ and $y$, then…

Given a semilattice $X$ we study the algebraic properties of the semigroup $\upsilon(X)$ of upfamilies on $X$. The semigroup $\upsilon(X)$ contains the Stone-Cech extension $\beta(X)$, the superextension $\lambda(X)$, and the space of…

Let $G$ be an affine algebraic group over an algebraically closed field $k$ of characteristic zero. In this paper, we consider finite $G$-equivariant morphisms $F:X\to Y$ of irreducible affine $G$-varieties. First we determine under which…

Let A,B be two random subsets of a finite group G. We consider the event that the products of elements from A and B span the whole group; i.e. (AB union BA) = G. The study of this event gives rise to a group invariant we call \Theta(G).…

We generalize the Davenport transform and use it to prove that, for a (possibly non-commutative) cancellative semigroup $\mathbb A = (A, +)$ and non-empty subsets $X,Y$ of $A$ such that the subsemigroup generated by $Y$ is commutative, we…

The order sequence of a finite group $G$ is a non-decreasing finite sequence formed of the element orders of $G$. Several properties of order sequences were studied by P. J. Cameron and H. K. Dey in a recent paper that concludes with a list…

Purpose: To develop the algebraic foundation of finite commutative ternary $\Gamma$-semirings by identifying their intrinsic invariants, lattice organization, and radical behavior that generalize classical semiring and $\Gamma$-ring…

We consider here one-parameter semigroups ${\bf T}=(T(t))_{t>0}$ of bounded operators on a Banach space $X$ which are weakly continuous in the sense of Arveson. For such a semigroup ${\bf T}$ denote by ${\mathcal M}_{\omega_{\bf T}}$ the…

We study a characteristic subgroup of finitely generated groups, consisting of elements with uniform upper bound for word-lengths. For a group $G$, we denote this subgroup by $G_{bound}$. We give sufficient criteria for triviality and…

Since its introduction by Symons, the semigroup of maps with restricted range has been studied in the context of transformations on a set, or of linear maps on a vector space. Sets and vector spaces being particular examples of independence…

The affine line and the punctured affine line over a finite field F are taken as benchmarks for the problem of describing geometric \'etale fundamental groups. To this end, using a reformulation of Tannaka duality we construct for a…

A finite group $G$ admits an {\em oriented regular representation} if there exists a Cayley digraph of $G$ such that it has no digons and its automorphism group is isomorphic to $G$. Let $m$ be a positive integer. In this paper, we extend…

A congruence $\varepsilon$ on a semigroup $S$ is perfect if for any congruence classes $x\varepsilon$ and $y\varepsilon$ their product as subsets of $S$ coincides (as a set) with the congruence class $(xy)\varepsilon$. Perfect congruences…

In this paper we describe the Greens relations on the semigroup of bi-ideals of ordered full transformation semigroup in terms of Greens relations of ordered full transformation semigroup on a set.

We determine the rings of invariants in the symmetric algebra on the dual of a vector space V over the field of two elements, for the group G of orthogonal transformations preserving a non-singular quadratic form on V. The invariant ring is…

We study integrality over rings (all commutative in this paper) and over ideal semifiltrations (a generalization of integrality over ideals). We begin by reproving classical results, such as a version of the "faithful module" criterion for…

Let $G$ be a finite group acting transitively on a set $\Omega$. We study what it means for this action to be {\it quasirandom}, thereby generalizing Gowers' study of quasirandomness in groups. We connect this notion of quasirandomness to…

Let $\mathcal C$ be a class of topological semigroups. A semigroup $X$ is called (1) $\mathcal C$-$closed$ if $X$ is closed in every topological semigroup $Y\in\mathcal C$ containing $X$ as a discrete subsemigroup, (2) $ideally$ $\mathcal…

This paper contains the more significant part of the article with the same title that will appear in the Volume 12 of Journal of Group Theory (2009). In this paper we determine all algebraic transformation groups $G$, defined over an…

An algebraic structure is said to be congruence permutable if its arbitrary congruences $\alpha$ and $\beta$ satisfy the equation $\alpha \circ \beta =\beta \circ \alpha$, where $\circ$ denotes the usual composition of binary relations. For…