Automorphisms of one-rooted trees: Growth, circuit structure, and acyclicity

By Said Najati Sidki. 2000

152 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/82329046bb77f9a47a37aa54350d08c3cc92a05e

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In Computational Theory and Mathematics

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Citations in the corpus

On a free group of transformations defined by an automaton (2006, background): “for some h ∈ S (R) implies that w2 = g(w1) for some g ∈ S(A).”
Automata and Square Complexes (2003, background): “Sidki suggested [ Sid00 ] one specific automaton A (one of the automata appearing in [Ale83]) as a candidate for generating a free group.”
On amenability of automata groups (2008, methodology): “hich the inﬁmum of the growth rates is 1 (also see [Wil04]). All of these groups are subgroups of BA. 2. Bounded automata In this Section we recall some standard facts about automata, see [GNS00] and [Sid00] for further details. 2.A. Automata and automorphisms. Deﬁnition 2.1. An automaton Π is a map”
Amenability of linear-activity automaton groups (2009, background): “In particular, in contrast with all known finitely generated non-amenable groups, Sidki (2000) showed that polynomial automaton groups have no free subgroups.”
Finite Automata of Polynomial Growth do Not Generate A Free Group (2004, background): “This observation and the fact that finite automata have either polynomial or exponential growth lead us to conjecture in [ 3 ] that free groups of rank 2 cannot be generated by finite automata of polynomial growth.”
Classification of groups generated by 3-state automata over a 2-letter alphabet (2008, background): “The class of polynomially growing automata was introduced by Sidki in [ Sid00 ].”
Some topics in the dynamics of group actions on rooted trees (2011, background): “Interesting classes of automata and the corresponding classes of groups were introduced by Sidki [172]; these are the classes of polynomially growing automata and groups generated by these automata.”
Dimension and randomness in groups acting on rooted trees (2002, background): “one of the simplest examples of elements of Γ(p) that are given by ﬁnite automata. Groups generated by such elements include Grigorchuk’s group, and have a rich theory, see Grigorchuk et al. (2000b). Sidki (2000) showed that s and another element given by a ﬁnite automaton cannot generate a free sub”
Hausdorff dimension in a family of self-similar groups (2006, background): “It served as a prime example and inspiration leading to the definition of many important classes of groups, such as branch groups, self-similar groups, finitely constrained groups, groups with L-presentations, groups generated by bounded automata, contracting groups, and so on (for more details see ”
Extensive amenability and an application to interval exchanges (2015, background): “roups generated by ﬁnite automata of polynomial activity. These are a well-studied class of groups acting on rooted trees, which can be classiﬁed according to their activity degree d ∈ N (we refer to [Sid00] for details). Amenability of polynomial activity automata groups is an open problem, that ha”
Schreier graphs of the Basilica group (2009, background): “He showed in [14] that a finite invertible automaton is bounded if and only if any two non-trivial cycles in the Moore diagram of the automaton are disjoint and not connected by a directed path.”