Related papers: On hereditarily just infinite profinite groups wit…

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…

Previous work has shown that the Hausdorff dimension of sofic affine-invariant sets is expressed as a limit involving intricate matrix products. This limit has typically been regarded as incalculable. However, in several highly non-trivial…

We prove that for every finitely-presented group G there exists a 2-dimensional irreducible complex-projective variety W with the fundamental group G, so that all singularities of W are normal crossings and Whitney umbrellas.

We study fibers of word maps in finite, profinite, and residually finite groups. Our main result is that, for any word w in the free group on d generators, there exists $\epsilon > 0$ such that if G is a residually finite group with…

This article provides a method to calculate the fixed-point proportion of any iterated wreath product acting on a $d$-regular tree. Moreover, the method applies to a generalization of iterated wreath products acting on a $d$-regular tree,…

For each prime p and a monic polynomial f, invertible over p, we define a group G_{p,f} of p-adic automorphisms of the p-ary rooted tree. The groups are modeled after the first Grigorchuk group, which in this setting is the group…

We consider the family of CIFSs of generalized complex continued fractions with a complex parameter space. This is a new interesting example to which we can apply a general theory of infinite CIFSs and analytic families of infinite CIFSs.…

We determine the lower rank of the direct product of finitely many hereditarily just infinite profinite groups of finite lower rank.

Let $\mathcal{S}$ be a sequence of finite perfect transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated wreath product in product action of the groups in $\mathcal{S}$ is…

Let $G$ be a finitely generated pro-$p$ group of positive rank gradient. Motivated by the study of Hausdorff dimension, we show that finitely generated closed subgroups $H$ of infinite index in $G$ never contain any infinite subgroups $K$…

We show that a profinite group with the same first-order theory as the direct product over all odd primes $p$ of the dihedral group of order $2p$, is necessarily isomorphic to this direct product.

We study the Hausdorff dimension of R-analytic subgroups in an R-analytic profinite group, where R is a pro-p ring whose asso- ciated graded ring is an integral domain. In particular, we prove that the set of such Hausdorff dimensions is a…

Let $(G_n,X_n)$ be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated permutational wreath product $...\wr G_2\wr G_1$ is topologically finitely generated if…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

Starting with an integral domain $D$ of characteristic $0$, we consider a class of iterated wreath product $W_n$ of $n$ copies of $D$. In order that $W_n$ be transfinite hypercentral, it is necessary to restrict to the case of wreath…

We study the dimension theory of limit sets of iterated function systems consisting of a countably infinite number of contractions. Our primary focus is on the intermediate dimensions: a family of dimensions depending on a parameter $\theta…

We prove that if G_P is a finitely constrained group of binary rooted tree automorphisms (a group binary tree subshift of finite type) defined by an essential pattern group P of pattern size d, d>1, and if G_P has maximal Hausdorff…

In the 1980's K.S. Brown proved that the Houghton group $H_n$ is of type $\operatorname{F}_{n-1}$ but not $\operatorname{FP}_n$. We show that, provided $n\ge3$, the same conclusion holds for all subgroups $G$ of $H_n$ that are 'large' in…

This paper establishes strong profinite rigidity results for K\"ahler groups, showing that certain groups are determined within the class of residually finite K\"ahler groups by their profinite completion. Examples include products of…

We characterize which permutational wreath products W^(X)\rtimes G are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the…