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Journals and Conferences
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 to the whole class are formulated. In particular, all finite, abelian, and free groups are classified. In addition, we provide detailed information and complete proofs for several… (More)
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples. For instance, all infinite Burnside automaton groups in the literature are generated by non reversible Mealy automata and it was recently shown that 2-state invertible-reversible… (More)
We construct a family of automata with n states, n ≥ 4, acting on a rooted binary tree that generate the free products of cyclic groups of order 2.
We study Sushchansky p-groups introduced in [Sus79]. We recall the original definition and translate it into the language of automata groups. The original actions of Sushchansky groups on p-ary tree are not level-transitive and we describe their orbit trees. This allows us to simplify the definition and prove that these groups admit faithful… (More)
Classification of groups generated by 3-state automata over a 2-letter alphabet started in [BGK06] is continued.
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group G on the subtrees corresponding to the orbits of G on levels of the tree. The connection between G and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work.
We provide a self-similar measure for the self-similar group G acting faithfully on the binary rooted tree, defined as the iterated monodromy group of the quadratic polynomial z + i. We also provide an Lpresentation for G and calculations related to the spectrum of the Markov operator on the Schreier graph of the action of G on the orbit of a point on the… (More)
The Schreier graphs of Thompson’s group F with respect to the stabilizer of 12 and generators x0 and x1, and of its unitary representation in L2([0, 1]) induced by the standard action on the interval [0, 1] are explicitly described. The coamenability of the stabilizers of any finite set of dyadic rational numbers is established. The induced subgraph of the… (More)