20 citations · 44 across the 13 of their papers we have counts for
17 papers
Stallings foldings for rational subsets of automatic groups
Lucía Asencio-Martín, John R. Britnell, Andrew Duncan +2
Let be an automatic group with associated regular language . We describe a procedure for constructing an automaton which recognises elements of a given submonoid or rational…
Bireversible automata generating lamplighter groups
Dominik Francoeur
For every non-trivial finite abelian group , we exhibit a bireversible automaton generating the lamplighter group .
On quasi-2-transitive actions of branch groups
Dominik Francoeur
An action of a group on a set is said to be quasi-n-transitive if the diagonal action of on has only finitely many orbits. We show that branch groups, a special c…
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…
On the Orbits of Automaton Semigroups and Groups
Daniele D'Angeli, Dominik Francoeur, Emanuele Rodaro +1
We investigate the orbits of automaton semigroups and groups to obtain algorithmic and structural results, both for general automata but also for some special subclasses. First, we…
On the stabilisers of points in groups with micro-supported actions
Dominik Francoeur
Given a group of homeomorphism of a first-countable Hausdorff space , we prove that if the action of on is minimal and has rigid stabilisers that…
Maximal subgroups of non-torsion Grigorchuk-Gupta-Sidki groups
Dominik Francoeur, Anitha Thillaisundaram
A Grigorchuk-Gupta-Sidki (GGS-)group is a subgroup of the automorphism group of the -adic tree for an odd prime , generated by one rooted automorphism and one directed automo…
On maximal subgroups of infinite index in branch and weakly branch groups
Dominik Francoeur
We generalise a technical tool, originally developed by Pervova for the study of maximal subgroups in Grigorchuk and GGS groups, to all weakly branch groups satisfying a natural co…
Commensurated subgroups and micro-supported actions
Pierre-Emmanuel Caprace, Adrien Le Boudec, Dominik Francoeur
Let be a finitely generated group and be a minimal compact -space. We assume that the -action is micro-supported, i.e. for every non-empty open subset …
Foliations between crooked planes in 3-dimensional Minkowski space
Jean-Philippe Burelle, Dominik Francoeur
We show that any two disjoint crooked planes in R^3 are leaves of a crooked foliation. This answers a question asked by Charette and Kim.
Infinite Automaton Semigroups and Groups Have Infinite Orbits
Daniele D'Angeli, Dominik Francoeur, Emanuele Rodaro +1
We show that an automaton group or semigroup is infinite if and only if it admits an -word (i. e. a right-infinite word) with an infinite orbit, which solves an open problem com…
On the existence of free subsemigroups in reversible automata semigroups
Dominik Francoeur, Ivan Mitrofanov
We prove that the semigroup generated by a reversible Mealy automaton contains a free subsemigroup of rank two if and only if it contains an element of infinite order.
Infinite finitely generated automata semigroups have infinite orbits
Dominik Francoeur
We prove that the semigroup generated by a finite state Mealy automaton is infinite if and only if there exists some right-infinite word in the alphabet w…
On the subexponential growth of groups acting on rooted trees
Dominik Francoeur
We show that every group in a large family of (not necessarily torsion) spinal groups acting on the ternary rooted tree is of subexponential growth.
Einstein tori and crooked surfaces
Jean-Philippe Burelle, Virginie Charette, Dominik Francoeur +1
In hyperbolic space, the angle of intersection and distance classify pairs of totally geodesic hyperplanes. A similar algebraic invariant classifies pairs of hyperplanes in the Ein…
Maximal subgroups of groups of intermediate growth
Dominik Francoeur, Alejandra Garrido
Finding the number of maximal subgroups of infinite index of a finitely generated group is a natural problem that has been solved for several classes of `geometric' groups (linear…
Fundamental domains in the Einstein Universe
Virginie Charette, Dominik Francoeur, Rosemonde Lareau-Dussault
We will discuss fundamental domains for actions of discrete groups on the 3-dimensional Einstein Universe. These will be bounded by crooked surfaces, which are conformal compactifi…