Related papers: A remark about supramenability and the Macaev norm

We build an analogue of the Gromov boundary for any proper geodesic metric space, hence for any finitely generated group. More precisely, for any proper geodesic metric space $X$ and any sublinear function $\kappa$, we construct a boundary…

In this paper one construction of composition formations was introduced. This construction contains formations of quasinilpotent groups, $c$-supersoluble groups, groups defined by ranks of chief factors and some new classes of groups. A…

Let $P \subset \mathbb{R}^{d}$ be a closed convex cone. Assume that $P$ is pointed, i.e. the intersection $P \cap -P=\{0\}$ and $P$ is spanning, i.e. $P-P=\mathbb{R}^{d}$. Denote the interior of $P$ by $\Omega$. Let $E$ be a product system…

In this work, we establish a mixed local--nonlocal Sobolev-type inequality in the Heisenberg group and demonstrate that its extremals coincide with solutions to the corresponding mixed local--nonlocal singular $p$-Laplace equations. We…

For a subgroup $S$ of a group $G$, let $I_G(S)$ denote the set of commutators $[g,s]=g^{-1}g^s$, where $g\in G$ and $s\in S$, so that $[G,S]$ is the subgroup generated by $I_G(S)$. We prove that if $G$ is a $p$-soluble finite group with a…

In this paper we study the generic, i.e., typical, behavior of finitely generated subgroups of hyperbolic groups and also the generic behavior of the word problem for amenable groups. We show that a random set of elements of a nonelementary…

This paper shows that divisible abelian torsion groups are realizable as Brauer groups of quasilocal fields. It describes the isomorphism classes of Brauer groups of primarily quasilocal fields and solves the analogous problem concerning…

We define H\"older classes $\Lambda_\alpha$ associated with a Markovian semigroup and prove that, when the semigroup satisfies the $\Gamma^2 \geq 0$ condition, the Riesz transforms are bounded between the H\"older classes. As a consequence,…

If E is a locally convex topological vector space, let P(E) be the pre-ordered set of all continuous seminorms on E. We study, on the one hand, for g an infinite cardinal those locally convex spaces E which have the g-neighbourhood property…

Assuming that every hyperbolic group is residually finite, we prove the congruence subgroup property for mapping class groups of hyperbolic surfaces of finite type. Under the same assumption, it follows that profinitely equivalent…

Let $G$ be a torsion-free, finitely-generated, nilpotent and metabelian group. In this work we show that $G$ embeds into the group of orientation preserving $C^{1+\alpha}$-diffeomorphisms of the compact interval, for all $\alpha< 1/k$ where…

For an uncountable cardinal \tau and a subset S of an abelian group G, the following conditions are equivalent: (i) |{ns:s\in S}|\ge \tau for all integers n\ge 1; (ii) there exists a group homomorphism \pi:G\to T^{2^\tau} such that \pi(S)…

Shumyatsky and the second author proved that if G is a finitely generated residually finite p-group satisfying a law, then, for almost all primes, the fact that a normal and commutator-closed set of generators satisfies a positive law…

In this paper we further study links between concentration of measure in topological transformation groups, existence of fixed points, and Ramsey-type theorems for metric spaces. We prove that whenever the group $\Iso(\U)$ of isometries of…

We show that the finitely generated simple left orderable groups $G_{\rho}$ constructed by the first two authors in arXiv:1807.06478 are uniformly perfect - each element in the group can be expressed as a product of three commutators of…

Let G be a finite group. We systematically exploit general homological methods in order to reduce the computation of G-equivariant KK-theory to topological equivariant K-theory. The key observation is that the functor assigning to a…

Recall that a locally compact group G is called unimodular if the left Haar measure on G is equal to the right one. It is proved in this paper that G is unimodular iff it is approximable by finite quasigroups (Latin squares).

We show that two uniform lattices of a regular right-angled Fuchsian building are commensurable, provided the chamber is a polygon with at least six edges. We show that in an arbitrary Gromov-hyperbolic regular right-angled building…

Gray and Ruskuc have shown that any group G occurs as the maximal subgroup of some free idempotent generated semigroup IG(E) on a biordered set of idempotents E, thus resolving a long standing open question. Given the group G, they make a…

A quasi-representation of a group is a map from the group into a matrix algebra (or similar object) that approximately satisfies the relations needed to be a representation. Work of many people starting with Kazhdan and Voiculescu, and…