Related papers: Liftable self-similar groups and scale groups

We find a condition on the acylindrical action of a finitely presented group on a simplicial tree which guarantees that this action will be dominated by an acylindrical action with finitely generated edge stabilisers, and find the first…

We consider finite group-actions on 3-manifolds $\cal H_g$ obtained as the connected sum of $g$ copies of $S^2 \times S^1$, with free fundamental group $F_g$ of rank $g$. We prove that, for $g > 1$, a finite group of diffeomorphisms of…

We introduce invertible subalgebras of local operator algebras on lattices. An invertible subalgebra is defined to be one such that every local operator can be locally expressed by elements of the inveritible subalgebra and those of the…

We verify a conjecture of Vershik by showing that Hall's universal countable locally finite group can be embedded as a dense subgroup in the isometry group of the Urysohn space and in the automorphism group of the random graph. In fact, we…

We introduce and study \emph{shift-similar} groups $G\le\textrm{Sym}(\mathbb{N})$, which play an analogous role in the world of Houghton groups that self-similar groups play in the world of Thompson groups. We also introduce Houghton-like…

We prove an accessibility theorem for finite-index splittings of groups. Given a finitely presented group G there is a number n(G) such that, for every reduced locally finite G-tree T with finitely generated stabilizers, T/G has at most…

In this note we study the finite groups whose subgroup lattices are dismantlable.

We introduce the Pythagorean dimension: a natural number (or infinity) for all representations of the Cuntz algebra and certain unitary representations of the Richard Thompson groups called Pythagorean. For each natural number d we…

We are concerned with orderable groups and particularly those with orderings invariant not only under multiplication, but also under a given automorphism or family of automorphisms. Several applications to topology are given: we prove that…

Reidemeister numbers of group automorphisms encode the number of twisted conjugacy classes of groups and might yield information about self-maps of spaces related to the given objects. Here we address a question posed by Gon\c{c}alves and…

In this note, we consider the $d$-cluster-tilted algebras, the endomorphism algebras of $d$-cluster-tilting objects in $d$-cluster categories. We show that a tilting module over such an algebra lifts to a $d$-cluster-tilting object in this…

This paper was motivated by a remarkable group, the maximal subgroup $M=S_3\ltimes 2^{2+1}_{-}\ltimes3^{2+1}\ltimes2^{6+1}_{-}$ of the sporadic simple group ${\rm Fi}_{23}$, where $S_3$ is the symmetric group of degree 3, and $2^{2+1}_{-}$,…

Consider an infinite tree. A hierarchomorphism (spheromorphism) is a homeomorphism of the absolute which can be extended to the tree except a finite subtree. Examples of groups of hierarchomorphisms: groups of locally analitic…

The class of locally compact near abelian groups is introduced and investigated as a class of metabelian groups formalizing and applying the concept of scalar multiplication. The structure of locally compact near abelian groups and its…

We present obstruction results for self-similar groups regarding the generation of free groups. As a main consequence of our main results, we solve an open problem posed by Grigorchuk by showing that in an automaton group where a…

We observe that, for each positive integer n > 2, each of the Artin groups of finite type A_n, B_n=C_n, and affine type \tilde A_{n-1} and \tilde C_{n-1} is a central extension of a finite index subgroup of the mapping class group of the…

This work continues the study of the properties of finitely constrained groups of binary tree automorphisms in terms of their Hausdorff dimension. We prove that there are exactly $2^{2d-3}$ finitely constrained groups of binary tree…

A necessary ingredient for our previous results on the form of the long distance effective action of the twisted lattice N=4 super Yang-Mills theory is the existence of a real space renormalization group which preserves the lattice…

The Solomon-Tits theorem says that the poset of proper non-trivial subspaces of a finite-dimensional vector space has realisation equivalent to a wedge of spheres. In this paper we prove a variant of this result for collections of geodesic…

Let $L$ be the function field of a projective space ${\mathbb P}^n_k$ over an algebraically closed field $k$ of characteristic zero, and $H$ be the group of projective transformations. An $H$-sheaf ${\mathcal V}$ on ${\mathbb P}^n_k$ is a…