8 citations · 35 across the 15 of their papers we have counts for
15 papers
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…
Limits of Rauzy graphs of languages with subexponential complexity
Paul-Henry Leemann, Tatiana Nagnibeda, Alexandra Skripchenko +1
To a subshift over a finite alphabet, one can naturally associate an infinite family of finite graphs, called its Rauzy graphs. We show that for a subshift of subexponential comple…
On the structure of finitely generated subgroups of branch groups
Dominik Francoeur, Rostislav Grigorchuk, Paul-Henry Leemann +1
We describe the block structure of finitely generated subgroups of branch groups with the so-called subgroup induction property, including the first Grigorchuk group …
Most rigid representation and Cayley index of finitely generated groups
Paul-Henry Leemann, Mikael de la Salle
If is a group and a generating set, canonically embeds into the automorphism group of its Cayley graph and it is natural to try to minimize, over all generating sets, t…
Wreath products of groups acting with bounded orbits
Paul-Henry Leemann, Grégoire Schneeberger
If is a subcategory of metric spaces, we say that a group G has property if any isometric action on an -space has bounded orbits. Examples of…
Property FW and wreath products of groups: a simple approach using Schreier graphs
Paul-Henry Leemann, Grégoire Schneeberger
The group property FW stands in-between the celebrated Kazdhan's property (T) and Serre's property FA. Among many characterizations, it might be defined, for finitely generated gro…
Subgroup induction property for branch groups
Dominik Francoeur, Paul-Henry Leemann
The subgroup induction property is a property of self-similar groups acting on rooted trees introduced by Grigorchuk and Wilson in 2003 that appears to have strong implications on…
Up to a double cover, every regular connected graph is isomorphic to a Schreier graph
Paul-Henry Leemann
We prove that every connected locally finite regular graph has a double cover which is isomorphic to a Schreier graph.
Cayley graphs with few automorphisms: the case of infinite groups
Paul-Henry Leemann, Mikael de la Salle
We characterize the finitely generated groups that admit a Cayley graph whose only automorphisms are the translations, confirming a conjecture by Watkins from 1976. The proof relie…
Finitely generated subgroups of branch groups and subdirect products of just infinite groups
Rostistlav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda
The aim of this paper is to describe the structure of the finitely generated subgroups of a family of branch groups, which includes the first Grigorchuk group and the Gupta-Sidki 3…
Weakly maximal subgroups of branch groups
Paul-Henry Leemann
Let be a branch group acting by automorphisms on a rooted tree . Stabilizers of infinite rays in are examples of weakly maximal subgroups of (subgroups that are maxi…
Cayley graphs with few automorphisms
Paul-Henry Leemann, Mikael de la Salle
We show that every finitely generated group G with an element of order at least admits a locally finite directed Cayley graph with automorphism group equal to G.…
Schreier graphs: transitivity and coverings
Paul-Henry Leemann
We give a characterization of isomorphisms between Schreier graphs in terms of the groups, subgroups and generating systems. This characterization may be thought as a graph analog…
Weakly maximal subgroups in regular branch groups
Khalid Bou-Rabee, Paul-Henry Leemann, Tatiana Nagnibeda
Let be a finitely generated regular branch group acting by automorphisms on a regular rooted tree . It is well-known that stabilizers of infinite rays in (aka parabolic…
Lamplighter groups, de Bruijn graphs, spider-web graphs and their spectra
Rostislav Grigorchuk, Paul-Henry Leemann, Tatiana Nagnibeda
We describe the infinite family of spider-web graphs , , and , studied in physical literature as tensor products of well-known de Brujin…