2 citations · 4 across the 16 of their papers we have counts for
19 papers
Uncountably many local isomorphism types of compactly generated simple groups
Ilaria Castellano, Jorge Fariña-Asategui, Mikel Eguzki Garciarena +7
A major open question in the theory of locally compact groups is the following. Let be the class of non-discrete compactly generated totally disconnected locally comp…
Corrigendum and addendum to "Fixed-point-free elements of iterated monodromy groups" [Trans. of the American Mathematical Society Vol. 367, No. 3 (2015), 2023-2049]
Jorge Fariña-Asategui, Rafe Jones, Santiago Radi
In this note we document a gap in an argument in the above paper, and point to new work in the literature giving a complete proof of the main result.
Arboreal Galois representations of rational functions: fixed-point proportion and the extension problem
Jorge Fariña-Asategui
We give an explicit description of the arithmetic-geometric extension of iterated Galois groups of rational functions. This yields a complete solution to the extension problem when…
Virtual retracts in groups acting on rooted trees
Jorge Fariña-Asategui, Jon Merladet Urigüen
We study virtual retracts in groups acting on rooted trees. We show that finitely generated branch groups do not have the local retraction (LR) property. Furthermore, we specialize…
Fixed-point proportion of geometric iterated Galois groups
Jorge Fariña-Asategui, Santiago Radi
In 1980, Odoni initiated the study of the fixed-point proportion of iterated Galois groups of polynomials motivated by prime density problems in arithmetic dynamics. The main goal…
Non-closed subgroups of weakly branch groups
Jorge Fariña-Asategui, Paul-Henry Leemann, Tatiana Nagnibeda
For a weakly branch group acting on a regular enough rooted tree, we provide two constructions of continuous families of distinct subgroups that are not closed in the profinite…
Random subgroups of branch groups
Jorge Fariña-Asategui, Santiago Radi
We show that independent Haar-random elements in a super strongly fractal branch profinite group generate a free subgroup acting freely on the boundary of the tree. This improves a…
Weakly branch actions: first-order theory, rigidity and Boston's conjecture
Jorge Fariña-Asategui
We disprove a well-known conjecture of Boston (2000), which claims that a just-infinite pro- group is branch if and only if it admits a positive-dimensional embedding in the gro…
Arboreal representations of linear groups
Jorge Fariña-Asategui
Abért and Virág conjectured in 2005 that any embedding of a linear group over a pro- domain into the group of -adic automorphisms should be zero-dimensional. We prove t…
On a question of Abért and Virág
Jorge Fariña-Asategui
Abért and Virág proved in 2005 that the Hausdorff dimension of a non-trivial normal subgroup of a level-transitive 1-dimensional subgroup of the group of -adic automorphisms $W_…
Markov processes associated to fractal branch groups
Jorge Fariña-Asategui
The author introduced recently a new natural construction which associates a measure-preserving dynamical system to any fractal profinite group. Here, we investigate these measure-…
On finitely generated Hausdorff spectra of groups acting on rooted trees
Jorge Fariña-Asategui, Oihana Garaialde Ocaña, Jone Uria-Albizuri
We answer two longstanding questions of Klopsch (1999) and Shalev (2000) by proving that the finitely generated Hausdorff spectrum of the closure of a finitely generated regular br…
On the fixed-point proportion of self-similar groups
Jorge Fariña-Asategui, Santiago Radi
We prove that super strongly fractal groups acting on regular rooted trees have null fixed-point proportion. In particular, we show that the fixed-point proportion of an infinite f…
An algorithm to compute the Hausdorff dimension of regular branch groups
Jorge Fariña-Asategui
An explicit algorithm is given for the computation of the Hausdorff dimension of the closure of a regular branch group in terms of an arbitrary branch structure. We implement this…
Cyclicity, hypercyclicity and randomness in self-similar groups
Jorge Fariña-Asategui
We introduce the concept of cyclicity and hypercyclicity in self-similar groups as an analogue of cyclic and hypercyclic vectors for an operator on a Banach space. We derive a suff…
Branch actions and the structure lattice
Jorge Fariña-Asategui, Rostislav Grigorchuk
J. S. Wilson proved in 1971 an isomorphism between the structural lattice associated to a group belonging to his second class of groups with every proper quotient finite and the Bo…
Torsion elements in branch pro- groups
Jorge Fariña-Asategui, Santiago Radi
We show that the set of torsion elements of a topological group admitting a branch pro- quotient has Haar measure zero.
The Hausdorff dimension of the generalized Brunner-Sidki-Vieira Groups
Jorge Fariña-Asategui, Mikel E. Garciarena
We compute the Hausdorff dimension of the closure of the generalized Brunner-Sidki-Vieira group acting on the -adic tree for , providing the first examples of self-simil…
Restricted Hausdorff spectra of -adic automorphisms
Jorge Fariña-Asategui
Firstly, we completely determine the self-similar Hausdorff spectrum of the group of -adic automorphisms where is a prime power, answering a question of Grigorchuk. Indeed,…