Non-elementary amenable subgroups of automata groups

Kate Juschenko*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 languageEnglish (US)
Pages (from-to)35-45
Number of pages11
JournalJournal of Topology and Analysis
Issue number1
StatePublished - Mar 1 2018


  • Automata group
  • elementary amenable groups
  • groups acting on rooted trees

ASJC Scopus subject areas

  • Analysis
  • Geometry and Topology

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