Related papers: Some elementary amenable subgroups of interval exc…

We show that the group of bounded automatic automorphisms of a rooted tree is amenable, which implies amenability of numerous classes of groups generated by finite automata. The proof is based on reducing the problem to showing amenability…

In this paper we address the question: How many pairwise non-isomorphic extremely amenable groups are there which are separable metrizable or even Polish? We show that there are continuum many such groups. In fact we construct continuum…

We prove that every finitely generated soluble group which is not virtually abelian has a subgroup of one of a small number of types.

We examine Hilbert-Schmidt stability (HS-stability) of discrete amenable groups from several angles. We give a short, elementary proof that finitely generated nilpotent groups are HS-stable. We investigate the permanence of HS-stability…

This paper studies effective separability for subgroups of finitely generated nilpotent groups and more broadly effective subgroup separability of finitely generated nilpotent groups. We provide upper and lower bounds that are polynomial…

We study the group of all interval exchange transformations (IETs). We show that for every IET $S$, there exists a dense open set of admissible IETs that share a relation with $S$. This is an extension of a result published by Dahmani,…

We define the notion of computability of F{\o}lner sets for finitely generated amenable groups. We prove, by an explicit description, that the Kharlampovich group, a finitely presented solvable group with unsolvable word problem, has…

We show that pointlike sets are decidable for the pseudovariety of finite semigroups whose idempotent-generated subsemigroup is R-trivial. Notably, our proof is constructive: we provide an explicit relational morphism which computes the…

We consider the Noether's problem on the noncommutative real rational functions invariant under the linear action of a finite group. For abelian groups the invariant skew-fields are always rational. We show that for a solvable group the…

We show that every free continuous action of a countably infinite elementary amenable group on a finite-dimensional compact metrizable space is almost finite. As a consequence, the crossed products of minimal such actions are…

We sharpen the orbit method for finite groups of small nilpotence class by associating representations to functionals on the corresponding Lie rings. This amounts to describing compatible intertwiners between representations parameterized…

We initiate a quantitative study of measure equivalence (and orbit equivalence) between finitely generated groups, which extends the classical setting of $\mathrm L^p$ measure equivalence. In this paper, our main focus will be on amenable…

This paper investigates the asymptotic behaviour of the minimal number of generators of finite index subgroups in residually finite groups. We analyze three natural classes of groups: amenable groups, groups possessing an infinite soluble…

We show that a finitely generated soluble group is virtually nilpotent if and only if the diameter of its finite coset spaces admits a uniform polynomial lower bound in terms of their size. We obtain the same conclusion for certain finitely…

We study the problem of realizing families of subgroups as the set of stabilizers of configurations from a subshift of finite type (SFT). This problem generalizes both the existence of strongly and weakly aperiodic SFTs. We show that a…

In this paper, we continue with the results in \cite{Pg} and compute the group of quasi-isometries for a subclass of split solvable unimodular Lie groups. Consequently, we show that any finitely generated group quasi-isometric to a member…

This paper introduces iterated monodromy groups for transcendental functions and discusses them in the simplest setting, for post-singularly finite exponential functions. These groups are self-similar groups in a natural way, based on an…

For any right-angled Artin group, we show that its outer automorphism group contains either a finite-index nilpotent subgroup or a nonabelian free subgroup. This is a weak Tits alternative theorem. We find a criterion on the defining graph…

We prove that a dense subgroup of $\mathrm{Homeo}_{+}(I)$ is not elementary amenable. We also show that the topological group $\mathrm{Homeo}_{+}(I)$ does not satisfy the Stability of the Generators Property, moreover, any finitely…

We describe groups elementarily equivalent to a free metabelian group with n generators. We also explore an exponentiation that naturally occurs in metabelian groups.