Related papers: Profinite semigroups

In this paper, we introduce the statistically multiplicative convergent sequences in locally solid Riesz algebras with respect to the algebra multiplication and the solid topology. We study on this concept and we give the notion of…

Diagram semigroups are interesting algebraic and combinatorial objects, several types of them originating from questions in computer science and in physics. Here we describe diagram semigroups in a general framework and extend our…

In this expanded account of a talk given at the Oberwolfach Arbeitsgemeinschaft "Totally Disconnected Groups", October 2014, we discuss results of Nikolay Nikolov and Dan Segal on abstract quotients of compact Hausdorff topological groups,…

It is well known that weakly continuous semigroups defined over $\mathbb{R}_{+}$ are automatically strongly continuous. We extend this result to more generally defined semigroups, including multiparameter semigroups.

We construct arithmetic Kleinian groups that are profinitely rigid in the absolute sense: each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. The Bianchi group…

In 1996 Jespers and Wang classified finite semigroups whose integral semigroup ring has finitely many units. In a recent paper, Iwaki-Juriaans-Souza Filho continued this line of research by partially classifying the finite semigroups whose…

By two well-known results, one of Ax, one of Lubotzky and van den Dries, a profinite group is projective iff it is isomorphic to the absolute Galois group of a pseudo-algebraically closed field. This paper gives an analogous…

In dynamical systems, shrinking target sets and pointwise recurrent sets are two important classes of dynamically defined subsets. In this article we introduce a mild condition on the linear parts of the affine mappings that allow us to…

In this paper we present a complete description of a stochastic semigroup of finite-dimensional projections in Hilbert space. The geometry of such semigroups is characterized by the asymptotic behavior of the widths of compact subsets with…

A profinite group is called small if it has only finitely many open subgroups of index n for each positive integer n. We show that every Frattini cover of a small profinite group is small. A profinite group is called strongly complete if…

We prove an effective equidistribution result for periodic orbits of semisimple groups on congruence quotients of an ambient semisimple group. This extends previous work of Einsiedler, Margulis and Venkatesh. The main new feature is that we…

Let w be a group-word. Suppose that the set of all w-values in a profinite group G is contained in a union of countably many cosets of subgroups. We are concerned with the question to what extent the structure of the verbal subgroup w(G)…

For a set of sorts $S$ and an $S$-sorted signature $\Sigma$ we prove that a profinite $\Sigma$-algebra, i.e., a projective limit of a projective system of finite $\Sigma$-algebras, is a retract of an ultraproduct of finite $\Sigma$-algebras…

Let $g$ be an element of a group $G$. For a positive integer $n$, let $E_n(g)$ be the subgroup generated by all commutators $[...[[x,g],g],\dots ,g]$ over $x\in G$, where $g$ is repeated $n$ times. We prove that if $G$ is a profinite group…

The Profinite Isomorphism Problem for a class of groups \mathcal{C} asks for an algorithm that decides for any two groups in \mathcal{C} whether they have isomorphic profinite completions. We present the positive solution to this problem…

In this series of three papers, we introduce and study cyclotomic pairs and smooth profinite groups. They are a geometric axiomatisation of Kummer theory for fields, with coefficients $p$-primary roots of unity, for a prime $p$. These…

This paper continues the investigation of non-zero determinants associated with finite semigroups containing a pair of non-commuting idempotents, as initiated in~\cite{Sha-Det2}. We focus on a class of semigroups, called \( \lll \)-smooth…

In this paper we investigate right uniform notion on some classes of semigroups. The main objective of this paper is realizing the structure of regular right uniform semigroups which can be applied as a cornerstone of characterizing regular…

We introduce an algebraic invariant for aperiodic inclusions of probability measure preserving equivalence relations. We use this invariant to prove that every stable orbit equivalence between free pmp actions of direct products of…

This paper is concerned with discrete, uniform subgroups (lattices) of oscillator groups, which are certain semidirect products of the Heisenberg group and the additive group of real numbers. The present paper rectifies the uncertainties in…