33 citations · 87 across the 16 of their papers we have counts for
17 papers · 1 filter
On Orbits and the Finiteness of Bounded Automaton Groups
Ievgen Bondarenko, Jan Philipp Wächter
We devise an algorithm which, given a bounded automaton A, decides whether the group generated by A is finite. The solution comes from a description of the infinite sequences havin…
Automaton groups and complete square complexes
Ievgen Bondarenko, Bohdan Kivva
The first example of a non-residually finite group in the classes of finitely presented small-cancelation groups, automatic groups, and CAT(0) groups was constructed by Wise as the…
Ends of Schreier graphs and cut-points of limit spaces of self-similar groups
Ievgen Bondarenko, Daniele D'Angeli, Tatiana Nagnibeda
Every self-similar group acts on the space of infinite words over some alphabet . We study the Schreier graphs for of the action of self-similar groups ge…
The lamplighter group generated by a bireversible automaton
I. Bondarenko, D. D'Angeli, E. Rodaro
We construct a bireversible self-dual automaton with states over an alphabet with letters which generates the lamplighter group .
On finite generation of self-similar groups of finite type
Ievgen V. Bondarenko, Igor O. Samoilovych
A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of…
The word problem in Hanoi Towers groups
Ievgen Bondarenko
We prove that elements of the Hanoi Towers groups have depth bounded from above by a poly-logarithmic function , where is the length of an elem…
Self-similar groups and the zig-zag and replacement products of graphs
Ievgen Bondarenko
Every finitely generated self-similar group naturally produces an infinite sequence of finite -regular graphs . We construct self-similar groups, whose graphs can be…
On a family of Schreier graphs of intermediate growth associated with a self-similar group
Ievgen Bondarenko, Tullio Ceccherini-Silberstein, Alfredo Donno +1
For every infinite sequence , with , we construct an infinite 4-regular graph . These graphs are precisely the Schreier graphs of the action of a…
Finite-state self-similar actions of nilpotent groups
Ievgen Bondarenko, Rostyslav Kravchenko
Let be a finitely generated torsion-free nilpotent group and be a surjective homomorphism from a subgroup of finite index with trivial -core. For ev…
Growth of Schreier graphs of automaton groups
Ievgen Bondarenko
Every automaton group naturally acts on the space of infinite sequences over some alphabet . For every we consider the Schreier graph of the action of the…
On the conjugacy problem for finite-state automorphisms of regular rooted trees
Ievgen V. Bondarenko, Natalia V. Bondarenko, Said N. Sidki +1
We study the conjugacy problem in the automorphism group of a regular rooted tree and in its subgroup of finite-state automorphisms. We show that under the c…
Finite generation of iterated wreath products
Ievgen Bondarenko
Let be a sequence of finite transitive permutation groups with uniformly bounded number of generators. We prove that the infinitely iterated permutational wreath produc…
Graph-directed systems and self-similar measures on limit spaces of self-similar groups
Ievgen Bondarenko, Rostyslav Kravchenko
Let be a group and be a contracting homomorphism from a subgroup of finite index. V.Nekrashevych [25] associated with the pair the limit dynamical syst…
Classification of groups generated by 3-state automata over a 2-letter alphabet
Ievgen Bondarenko, Rostislav Grigorchuk, Rostyslav Kravchenko +4
This article contains most of the known results on the classification of groups generated by 3-state automata over a 2-letter alphabet, extending the previous papers 0704.3876 and…
Groups generated by 3-state automata over a 2-letter alphabet, II
Ievgen Bondarenko, Rostislav Grigorchuk, Rostyslav Kravchenko +4
Classification of groups generated by 3-state automata over a 2-letter alphabet started in the first paper (see http://www.arxiv.org/abs/math/0612178) is continued.
Post-critically finite self-similar groups
Ievgen Bondarenko, Volodymyr Nekrashevych
We describe in terms of automata theory the automatic actions with post-critically finite limit space. We prove that these actions are precisely the actions by bounded automata and…
Groups generated by 3-state automata over a 2-letter alphabet, I
Ievgen Bondarenko, Rostislav Grigorchuk, Rostyslav Kravchenko +4
An approach to a classification of groups generated by 3-state automata over a 2-letter alphabet and the current progress in this direction are presented. Several results related t…