Amenability of quadratic automaton groups

Gideon Amir; Omer Angel; Balint Virag

Amenability of quadratic automaton groups

Gideon Amir
, Omer Angel
, Balint Virag

Department of Mathematics

Research output: Working paper / Preprint › Preprint

15 Downloads (Pure)

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 zero ray. These bounds, combined with results of \cite{JNS} 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	Undefined/Unknown
Publisher	arXiv preprint
State	Published - 30 Nov 2021

Bibliographical note

20 pages, 3 figures

Keywords

math.GR
math.PR
60B15, 43A07, 20E08

Access to Document

2111.15206v1

Cite this

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title = "Amenability of quadratic automaton groups",

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 zero ray. These bounds, combined with results of \textbackslash{}cite\{JNS\} 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. ",

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N2 - 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 zero ray. These bounds, combined with results of \cite{JNS} 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.

AB - 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 zero ray. These bounds, combined with results of \cite{JNS} 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.

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KW - 60B15, 43A07, 20E08

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BT - Amenability of quadratic automaton groups

PB - arXiv preprint

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