7 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…
Spinal Hanoi Towers Groups
Francesca Cavalieri, Mikel E. Garciarena, Marialaura Noce
We introduce and study \emph{spinal Hanoi towers groups}, a family of groups acting on the -adic tree that contains both the classical Hanoi towers group and…
A radical answer to a question by Robinson
Blaise Boissonneau, Mikel E. Garciarena, Immanuel Halupczok
We study the ring of Puiseux polynomials with integer coefficients. We prove notably that the order given by the leading coefficient is definable without parameters in the language…
On the lower central series of a large family of non-periodic GGS-groups
Gustavo A. Fernández-Alcober, Mikel E. Garciarena, Marialaura Noce
For an odd prime , we determine the lower central series of a large family of non-periodic GGS-groups, which has a density of roughly within all GGS-groups.…
Maximal subgroups in torsion branch groups
Mikel Eguzki Garciarena, J. Moritz Petschick
We study the maximal subgroups of branch groups and obtain a criterion that ensures that certain spinal groups are contained in the class of groups with all maximal…
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…
On verbal subgroups of the group of automorphisms of regular rooted trees
Costantino Delizia, Mikel E. Garciarena, Marialaura Noce
In this paper we revisit the description of all verbal subgroups of the group of automorphisms of a regular rooted tree , for and odd.