Related papers: Order separability
Free independence is an important tool for studying the structure of operator algebras. It is natural to ask from the model-theoretic standpoint whether free independence is captured well in first-order model theory via the notion of a…
Consider a random sample $X_1 , X_2 , ..., X_n$ drawn independently and identically distributed from some known sampling distribution $P_X$. Let $X_{(1)} \le X_{(2)} \le ... \le X_{(n)}$ represent the order statistics of the sample. The…
A joint characterisation of the controllability and observability of a particular kind of discrete system has been developed. The key idea of the procedure can be reduced to a correct choice of the sampling sequence. This freedom, owing to…
We show that in a Morse local-to-global group where stable subgroups are separable, the product of any stable subgroups is separable. As an application, we show that the product of stable subgroups in virtually special groups is separable.
A finite group $G$ is called $\psi$-divisible if $\psi(H)|\psi(G)$ for any subgroup $H$ of $G$, where $\psi(H)$ and $\psi(G)$ are the sum of element orders of $H$ and $G$, respectively. In this paper, we extend a result provided in [10], by…
In this paper, we study connections between the structure of a group and the structure of the group (under pointwise product) of its polynomial functions.
We prove new separability results about free groups. Namely, if $H_1, \ldots , H_k$ are infinite index, finitely generated subgroups of a non-abelian free group $F$, then there exists a homomorphism onto some alternating group $f:F…
We investigate the group $G \vee H$ obtained by gluing together two groups $G$ and $H$ at the neutral element. This construction curiously shares some properties with the free product but others with the direct product. Our results address…
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 classify the finite groups $G$ such that the group of units of the integral group ring ${\mathbb Z} G$ has a subgroup of finite index which is a direct product of free-by-free groups.
The object of observation in present paper is statistical independence of real sequences and its description as independence with re spect to certain class of densities.
A conjecture of Dicks and the author on rank of the intersection of factor-free subgroups in free products of groups is proved for the case of left ordered groups.
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.
In this article we raise some new questions about positive definite functions on free groups, and explain how these are related to more well-known questions. The article is intended as a survey of known results that also offers some new…
Known and new results on free Boolean topological groups are collected. An account of properties which these groups share with free or free Abelian topological groups and properties specific of free Boolean groups is given. Special emphasis…
We give a description of the model theoretic relation of forking independence in terms of the notion of JSJ decompositions in non abelian free groups.
In the present work, we continue the research initiated in the preprint: V. G. Bardakov, A. L. Iskra, Orders of products of horizontal class transpositions, arXiv:2409.13341, and related to S. Kohl's question on the orders of products of…
Given an ordered structure, we study a natural way to extend the order to preorders on type spaces. For definably complete, linearly ordered structures, we give a characterisation of the preorder on the space of 1-types. We apply these…
We show how to use topological ideas, such as compactness, to establish orderability properties of infinite groups. A new application is to provide a left-ordering for the group of PL homeomorphisms of a connected surface with boundary…
We show that in the category of preordered sets, there is a natural notion of pretorsion theory, in which the partially ordered sets are the torsion-free objects and the sets endowed with an equivalence relation are the torsion objects.…