Related papers: Branch Groups

We introduce the notion of a telescope of groups. Very roughly a telescope is a directed system of groups that contains various commuting images of some fixed group $B$. Telescopes are inspired from the theory of groups acting on rooted…

This is the second part of a series of three articles which introduce laminations for free groups (see math.GR/0609416 for the first part). Several definition of the dual lamination of a very small action of a free group on an $\R$-tree are…

We describe the block structure of finitely generated subgroups of branch groups with the so-called subgroup induction property, including the first Grigorchuk group $\mathcal{G}$ and the torsion GGS groups.

Group theory is a particularly fertile field for the design of practical algorithms. Algorithms have been developed across the various branches of the subject and they find wide application. Because of its relative maturity, computational…

We consider analogues of Grigorchuk-Gupta-Sidki (GGS-)groups acting on trees of growing degree; the so-called growing GGS-groups. These groups are not just infinite and do not possess the congruence subgroup property, but many of them are…

Lecture notes on tree language theory, in particular recognizable tree languages and finite state tree transformations.

The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relations are used to obtain one-parameter families of connected…

We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns closely with the notions of tree-depth and shrub-depth of graphs…

We explicitly determine the automorphism groups of all self-similar trees (a.k.a. trees with finitely many cone types). We show that any such automorphism group is a direct limit of certain finite products of finite symmetric groups, which…

We consider conjugation action of symmetric group on the semigroup of all partial functions and develop a machinery to investigate character formulas and multiplicities. In particular, we determine nilpotent matrices whose orbit under…

Traditional clustering identifies groups of objects that share certain qualities. Tangles do the converse: they identify groups of qualities that often occur together. They can thereby identify and discover 'types': of behaviour, views,…

The paper is devoted to the study of the lattice of subgroups of the Lamplighter type groups and to the relative gradient rank.

In this article we give a concept of ground subgroup for finite and countable groups. By our definition such a subgroup of a group depends on a given subset of the group and on a given partition of the subset. For finite and free groups we…

In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

We introduce "braided" versions of self-similar groups and R\"over--Nekrashevych groups, and study their finiteness properties. This generalizes work of Aroca and Cumplido, and the first author and Wu, who considered the case when the…

In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the…

To most mathematicians and computer scientists the word ``tree'' conjures up, in addition to the usual image, the image of a connected graph with no circuits. In the last few years various types of trees have been the subject of much…

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.

This article presents the construction of finitely generated branch groups with uncountably many maximal subgroups using embedding techniques. This addresses a question posed by Grigorchuk.

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…