Related papers: A note on free paratopological groups
Some examples and basic properties of ultrametric spaces are briefly discussed.
The aim of this paper is to show how free probability theory sheds light on spectral properties of deformed matricial models and provides a unified understanding of various asymptotic phenomena such as spectral measure description,…
This article is a survey article on geometric group theory from the point of view of a non-expert who likes geometric group theory and uses it in his own research. The sections are: classical examples, basics about quasiisometry,properties…
The main purpose of this paper is to describe some published results and outline corresponding approaches which when applied to automorphism groups of algebras or groups establish that these groups are linear or non-linear.
We consider metric versions of the notions of local embeddability and LEF. We pay special attention to normally finitely generated groups with word metrics.
We show that the geometric and homological finiteness properties of group pairs are invariant under a suitable notion of quasi-isometry for group pairs.
It is well-known that point-set topology (without additional structure) lacks the capacity to generalize the analytic concepts of completeness, boundedness, and other typically-metric properties. The ability of metric spaces to capture this…
In this paper, we introduce the notion of $L^2$-subgroup rigid groups and demonstrate that free groups are $L^2$-subgroup rigid. As a consequence, we establish the equivalence between compressibility, inertness, strong inertness, and…
In this paper we introduce and study the concept of normality degree of a finite group $G$. This quantity measures the probability of a random subgroup of $G$ to be normal. Explicit formulas are obtained for some particular classes of…
We use hyperbolic towers to answer some model theoretic questions around the generic type in the theory of free groups. We show that all the finitely generated models of this theory realize the generic type $p_0$, but that there is a…
Topological full groups originated from the theory of topological dynamical systems and have been having considerable impact on group theory in recent years. This text represents an introduction/survey on topological full groups. After…
We introduce the concept of a pants decomposition for a finitely generated free group and construct the corresponding pants graph. A pants decomposition of a free group leads to the formation of a simplicial graph, referred to as the pants…
This paper is a survey of some properties of the braid groups and related groups that lead to questions on mapping class groups.
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.
We give a survey on results regarding self-similar and automaton presentations of free groups and semigroups and related products. Furthermore, we discuss open problems and results with respect to algebraic decision problems in this area.
We discuss various modifications of separability, precompactnmess and narrowness in topological groups and test those modifications in the permutation groups $S(X)$ and $S_{<\omega}(X)$.
Recent results on finite open group transformations are reviewed.
We generalize the notion of isoperimetric profiles of finitely generated groups to their actions by measuring the boundary of finite subgraphings of the orbit graphing. We prove that like the classical isoperimetric profiles for groups,…
In this article, we study the outer automorphism group of a group G decomposed as a finite graph of group with finite edge groups and finitely generated vertex groups with at most one end. We show that Out(G) is essentially obtained by…
Consider a one-ended word-hyperbolic group. If it is the fundamental group of a graph of free groups with cyclic edge groups then either it is the fundamental group of a surface or it contains a finitely generated one-ended subgroup of…