Mathematische Annalen

, Volume 354, Issue 2, pp 765–785 | Cite as

Growth of Schreier graphs of automaton groups

  • Ievgen V. BondarenkoEmail author


Every automaton group naturally acts on the space X ω of infinite sequences over some alphabet X. For every \({w \in X^{\omega}}\) we consider the Schreier graph Γ w of the action of the group on the orbit of w. We prove that for a large class of automaton groups all Schreier graphs Γ w have subexponential growth bounded above by \({n^{(\log n)^m}}\) with some constant m. In particular, this holds for all groups generated by automata with polynomial activity growth (in terms of S. Sidki), confirming a conjecture of V. Nekrashevych. We present applications to ω-periodic graphs and Hanoi graphs.

Mathematics Subject Classification (2000)

20F65 05C25 20F69 


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Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Mechanics and Mathematics DepartmentNational Taras Shevchenko University of KyivKyivUkraine

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