Amenability of quadratic automaton groups

Gideon Amir; Omer Angel; Bálint Virág

doi:10.4171/GGD/821

Amenability of quadratic automaton groups

Gideon Amir, Omer Angel, Bálint Virág

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We give lower bounds for the electrical resistance between vertices in the Schreier graphs of the action of the linear (degree 1) and quadratic (degree 2) mother groups on the orbit of the 0-ray. These bounds, combined with results of Juschenko et al. (2016), show that every quadratic activity automaton group is amenable. The resistance bounds use an apparently new “weighted” version of the Nash-Williams criterion which may be of independent interest.

Original language	English
Pages (from-to)	169-185
Number of pages	17
Journal	Groups, Geometry, and Dynamics
Volume	19
Issue number	1
DOIs	https://doi.org/10.4171/GGD/821
State	Published - 2025

Bibliographical note

Publisher Copyright:
© 2024 European Mathematical Society.

Keywords

amenability
automaton group
Schreier graph

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10.4171/GGD/821

Cite this

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Amenability of quadratic automaton groups

Abstract

Bibliographical note

Keywords

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