%0 Journal Article
%T Amenability of Universal 2-Grigorchuk group
%A Roman Muchnik
%J Mathematics
%D 2005
%I arXiv
%X 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.
%U http://arxiv.org/abs/math/0505572v3