Related papers: Some non-contracting automata groups
We show that there is a sequence of subsets of each discrete Heisenberg group for which the non-singular ergodic theorem holds. The sequence depends only on the group; it works for any of its non-singular actions. To do this we use a metric…
We study the acylindrical hyperbolicity of the outer automorphism group of a right-angled Artin group $A_\Gamma$. When the defining graph $\Gamma$ has no SIL-pair (separating intersection of links), we obtain a necessary and sufficient…
We introduce a family of atomic measures on free groups generated by no-return random walks. These measures are shown to be very convenient for comparing "relative sizes" of subgroups, context-free and regular subsets (that, subsets…
In this paper we define a way to get a bounded invertible automaton starting from a finite graph. It turns out that the corresponding automaton group is regular weakly branch over its commutator subgroup, contains a free semigroup on two…
We study automaton groups without singular points, that is, points in the boundary for which the map that associates to each point its stabilizer, is not continuous. This is motivated by the problem of finding examples of infinite…
We use a semigroup-theoretic construction by Peter Higgins in order to produce, for each even $n$, an $n$-state and 3-letter synchronizing automaton with the following two features: 1) all its input letters act as idempotent selfmaps of…
We introduce new non-abelian zeta functions for curves defined over finite fields. There are two types, i.e., pure non-abelian zetas defined using semi-stable bundles, and group zetas defined for pairs consisting of (reductive group,…
We introduced a family of infinite graphs directly associated with a class of von Neumann automaton model A_{G}. These are finite state models used in symbolic dynamics: stimuli models and in control theory. In the context of groupoid von…
We exhibit free-by-cyclic groups containing non-free locally-free subgroups, including some word hyperbolic examples. We also show that these groups are not subgroup separable. We use Bestvina-Brady Morse theory in our arguments.
We develop an effective and natural approach to interpret any semigroup admitting a special language of greedy normal forms as an automaton semigroup,namely the semigroup generated by a Mealy automaton encoding the behaviour of such a…
A deterministic finite (semi)automaton is primitive if its transition monoid (semigroup) acting on the set of states has no non-trivial congruences. It is synchronizing if it contains a constant map (transformation). In analogy to…
The notion of an automaton over a changing alphabet $X=(X_i)_{i\geq 1}$ is used to define and study automorphism groups of the tree $X^*$ of finite words over $X$. The concept of bi-reversibility for Mealy-type automata is extended to…
We give a new characterization of primitive permutation groups tied to the notion of completely reachable automata. Also, we introduce sync-maximal permutation groups tied to the state complexity of the set of synchronizing words of certain…
We construct an example of an IA-automorphism of the free metabelian group of rank $n\geq 3$ without nontrivial fixed points. That gives a negative answer to the question raised by Shpilrain. By a result of Bachmuth \cite{Ba1}, such an…
We introduce a new class of semigroups arising from a restricted class of asynchronous automata. We call these semigroups "expanding automaton semigroups." We show that the class of synchronous automaton semigroups is strictly contained in…
We investigate properties which ensure that a given finite graph is the commuting graph of a group or semigroup. We show that all graphs on at least two vertices such that no vertex is adjacent to all other vertices is the commuting graph…
We proved that non-elementary discrete convergence groups are acylindrically hyperbolic.
In this paper we extend the construction of Giudici, Morgan and Zhou [arXiv:2110.07896] to give the first known examples of nonregular, $2$-closed permutation groups of rank greater than $4$ that are not the automorphism group of any…
There is empirical evidence supporting the claim that almost all cubic non-Hamiltonian graphs are bridge graphs. In this paper, we pose a related conjecture and prove that the original claim holds for non-3-connected graphs if the…
Higher dimensional automata, i.e. labelled precubical sets, model concurrent systems. We introduce the homology graph of an HDA, which is a directed graph whose nodes are the homology classes of the HDA. We show that the homology graph is…