Non-elementary amenable subgroups of automata groups

Kate Juschenko

doi:10.1142/S179352531850005X

Non-elementary amenable subgroups of automata groups

Kate Juschenko^*

^*Corresponding author for this work

Mathematics

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

7 Scopus citations

Abstract

We consider groups of automorphisms of rooted locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. We give a unified proof for all known examples of non-elementary amenable groups that act on the trees: groups of intermediate growths and Basilica group. Moreover, we show that all finitely generated branch groups are not elementary amenable, which was conjectured by Grigorchuk.

Original language	English (US)
Pages (from-to)	35-45
Number of pages	11
Journal	Journal of Topology and Analysis
Volume	10
Issue number	1
DOIs	https://doi.org/10.1142/S179352531850005X
State	Published - Mar 1 2018

Keywords

Automata group
elementary amenable groups
groups acting on rooted trees

ASJC Scopus subject areas

Analysis
Geometry and Topology

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10.1142/S179352531850005X

Cite this

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AB - We consider groups of automorphisms of rooted locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. We give a unified proof for all known examples of non-elementary amenable groups that act on the trees: groups of intermediate growths and Basilica group. Moreover, we show that all finitely generated branch groups are not elementary amenable, which was conjectured by Grigorchuk.

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KW - elementary amenable groups

KW - groups acting on rooted trees

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Non-elementary amenable subgroups of automata groups

Abstract

Keywords

ASJC Scopus subject areas

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