Non-elementary amenable subgroups of automata groups
Group Theory
2015-04-03 v1
Abstract
We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups are not elementary amenable, which was conjectured by Grigorchuk.
Keywords
Cite
@article{arxiv.1504.00610,
title = {Non-elementary amenable subgroups of automata groups},
author = {Kate Juschenko},
journal= {arXiv preprint arXiv:1504.00610},
year = {2015}
}