Amenability of Universal 2-Grigorchuk group
Group Theory
2007-05-23 v3 Combinatorics
Abstract
We consider the universal Grigorchuk 2-group, i.e., the group such that every Grigorchuk 2-group is a quotient. We show that this group has a nice universal representation in the group of all functions f:{0,1,2}^N --> Aut(T_2), where T_2 is a group of automorphism of the binary tree. Finally, we prove that this universal Grigorchuk 2-group is amenable. The proof is an application of the ``Munchhausen trick'' developed by V. Kaimanovich.
Keywords
Cite
@article{arxiv.math/0505572,
title = {Amenability of Universal 2-Grigorchuk group},
author = {Roman Muchnik},
journal= {arXiv preprint arXiv:math/0505572},
year = {2007}
}
Comments
10 pages