Related papers: Non-abelian group structure on the Urysohn space

We suggest an infinite-dimensional extension of the gauge transformations which includes non-Abelian tensor gauge fields. Extended gauge transformations of non-Abelian tensor gauge fields form a new large group which has natural geometrical…

Non-trivial braid-group representations appear as non-Abelian quantum statistics of emergent Majorana zero modes in one and two-dimensional topological superconductors. Here, we generate such representations with topologically protected…

We consider a number of examples of groups together with an infinite conjugation invariant generating set, including: the free group with the generating set of all separable elements; surface groups with the generating set of all…

We address the degree-diameter problem for Cayley graphs of Abelian groups (Abelian graphs), both directed and undirected. The problem turns out to be closely related to the problem of finding efficient lattice coverings of Euclidean space…

Some results that are true in classical groups are investigated in generalized groups and are shown to be either generally true in generalized groups or true in some special types of generalized groups. Also, it is shown that a Bol groupoid…

We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone $\cal R$ of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance…

Let $k$ be a nonarchimedean local field. For any $n\geq 3$, we construct the first examples of robust quasi-isometric embeddings of non-elementary free groups into $\mathsf{GL}_n(k)$ which are not limits of Anosov representations. If…

Let R denote the smallest class of compact spaces containing all metric compacta and closed under limits of continuous inverse sequences of retractions. Class R is striclty larger than the class of Valdivia compact spaces. We show that…

Let $G$ be a finite nonabelian group, and let $\psi:G\to G$ be a homomorphism with abelian image. We show how $\psi$ gives rise to two Hopf-Galois structures on a Galois extension $L/K$ with Galois group (isomorphic to) $G$; one of these…

We prove that the existence of a selective ultrafilter implies the existence of a countably compact Hausdorff group topology on the free Abelian group of size continuum. As a consequence, we show that the existence of a selective…

Let $D$ be a division ring with center $F$ and $N$ a subnormal subgroup of the multiplicative group $D^*$ of $D$. Assume that $N$ contains a non-abelian solvable subgroup. In this paper, we study the problem on the existence of non-abelian…

We mainly discuss the cardinal invariants and generalized metric properties on paratopological groups or rectifiable spaces, and show that: (1) If $A$ and $B$ are $\omega$-narrow subsets of a paratopological group $G$, then $AB$ is…

Recently, much interest was devoted to the Urysohn universal metric space U and its isometries; this paper is a contribution to this field of research. In particular, we study some properties of isometries of U, and prove the following…

Non-local gravity can potentially solve several problems of gravitational field both at Ultra-Violet and Infra-Red scales. However, such an approach has been formulated mainly in metric formalism. In this paper, we discuss non-local…

Given a countable group $G$, we develop a method to construct an overgroup $H$ that is finitely generated, highly transitive and mixed identity free. Our construction can be controlled to ensure that some fundamental group theoretic…

Given a countable, totally ordered commutative monoid $\mathcal{R}=(R,\oplus,\leq,0)$, with least element $0$, there is a countable, universal and ultrahomogeneous metric space $\mathcal{U}_\mathcal{R}$ with distances in $\mathcal{R}$. We…

In this note we consider a $p$-isometrisability property of discrete groups. If $p=2$ this property is equivalent to unitarisability. We prove that any group containing a non-abelian free subgroup is not $p$-isometrisable for any $p\in (1,…

Multi-Higgs models equipped with global symmetry groups, either exact or softly broken, offer a rich framework for constructions beyond the Standard Model and lead to remarkable phenomenological consequences. Knowing all the symmetry…

In this paper we study (logical) types and isotypical equivalence of torsion free Abelian groups. We describe all possible types of elements and standard 2-tuples of elements in these groups and classify separable torsion free Abelian…

A set of quasi-uniform random variables $X_1,...,X_n$ may be generated from a finite group $G$ and $n$ of its subgroups, with the corresponding entropic vector depending on the subgroup structure of $G$. It is known that the set of entropic…