On elementary amenable bounded automata groups
Group Theory
2018-01-09 v2
Abstract
There are several natural families of groups acting on rooted trees for which every member is known to be amenable. It is, however, unclear what the elementary amenable members of these families look like. Towards clarifying this situation, we here study elementary amenable bounded automata groups. We are able to isolate the elementary amenable bounded automata groups in three natural subclasses of bounded automata groups. In particular, we show that iterated monodromy groups of post-critically finite polynomials are either virtually abelian or not elementary amenable.
Keywords
Cite
@article{arxiv.1712.08418,
title = {On elementary amenable bounded automata groups},
author = {Kate Juschenko and Benjamin Steinberg and Phillip Wesolek},
journal= {arXiv preprint arXiv:1712.08418},
year = {2018}
}
Comments
Typos corrected, exposition improved, and proofs clarified