Related papers: Quasi-isometrically embedded subgroups of Thompson…

We present a method of coding general self-similar structures. In particular, we construct a symmetry group of a one-dimensional Thue-Morse quasicrystal, i.e., of a nonperiodic ground state of a certain translation-invariant, exponentially…

Thompson's group $V$ has a rich variety of subgroups, containing all finite groups, all finitely generated free groups and all finitely generated abelian groups, the finitary permutation group of a countable set, as well as many wreath…

In this second article, we continue to study classes of groups constructed from a functorial method due to Vaughan Jones. A key observation of the author shows that these groups have remarkable diagrammatic properties that can be used to…

We prove that a large class of metrizable group topologies for subgroups of $\mathbb{R}^n$ and the completions of the subgroups are locally isometric to, respectively, metrizable group topologies for $\mathbb{Z}$ and their completions,…

We develop a theory of type semigroups for arbitrary twisted, not necessarily Hausdorff \'etale groupoids. The type semigroup is a dynamical version of the Cuntz semigroup. We relate it to traces, ideals, pure infiniteness, and stable…

This paper is a more succinct version of the author's 1993 UCLA mathematics thesis. It proves that any group quasi-isometric to the product of the hyperbolic plane with the real line is a finite extension of a cocompact lattice in either…

In this paper we study the non-amenability question of the Thompson group $F$ from the $C^{*}$ algebra side. Using a characterization of amenability in this framework we set about evaluating the reduced norm of the averages $\frac{1}{n}\sum…

We study the semigroup $\textbf{{ID}}_{\infty}$ of all partial isometries of the set of integers $\mathbb{Z}$. It is proved that the quotient semigroup $\textbf{{ID}}_{\infty}/\mathfrak{C}_{\textsf{mg}}$, where $\mathfrak{C}_{\textsf{mg}}$…

For a finite group $G$ and a positive integer $n$, let $G(n)$ be the set of all elements in $G$ such that $x^{n}=1$. The groups $G$ and $H$ are said to be of the same (order) type if $G(n)=H(n)$, for all $n$. The main aim of this paper is…

We show that the group of all pl-homeomorphisms of the reals having bounded slopes surjects on the group $QI({\Bbb R})$ of all quasi-isometries of ${\Bbb R}$. We prove that the following groups can be imbedded in $QI({\Bbb R})$: The group…

Let G be a connected semisimple Lie group with at least one absolutely simple factor S such that R-rank(S) is at least 2, and let $\Gamma$ be a uniform lattice in G. (a) If $CH$ holds, then $\Gamma$ has a unique asymptotic cone up to…

We consider a class of groups $V_n(G)$ which are supergroups of the Higman-Thompson groups $V_n$. These groups fit in a framework of Elizabeth Scott for generating infinite virtually simple groups, and the groups we study in particular are…

We study the algebraic entropy of continuous endomorphisms of compactly covered, locally compact, topologically quasihamiltonian groups. We provide a Limit-free formula which helps us to simplify the computations of this entropy. Moreover,…

Suppose that a finitely generated group $G$ is hyperbolic relative to a collection of subgroups $\{H_1, ..., H_m\} $. We prove that if each of the subgroups $H_1, ..., H_m$ has finite asymptotic dimension, then asymptotic dimension of $G$…

In this paper it is proved that the group $F\left(\frac32\right)$, a Thompson-style group with breaks in $\mathbb{Z}\left[\frac16\right]$ but whose slopes are restricted only to powers of $\frac32$, is finitely generated, with a generating…

For a finitely generated group, there are two recent generalizations of the notion of a quasiconvex subgroup of a word-hyperbolic group, namely a stable subgroup and a Morse or strongly quasiconvex subgroup. Durham and Taylor defined…

Let $\frak{F}$ be a class of finite groups. A subgroup $H$ of a finite group $G$ is said to be $\mathfrak{F_{\mathrm s}}$-quasinormal in $G$ if there exists a normal subgroup $T$ of $G$ such that $HT$ is $s$-permutable in $G$ and $(H\cap…

We prove that the category of quasi-pseudometric modular spaces whose morphisms are the nonexpansive mappings is isomorphic to a quantale enriched category. To achieve this, we construct an appropriate quantale of isotone functions. We also…

In this paper, we construct embeddings of right-angled Artin groups into higher dimensional Thompson groups. In particular, we embed every right-angled Artin groups into n-dimensional Thompson group, where n is the number of complementary…

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse…