Amenability of Universal 2-Grigorchuk group
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:0,1,2N --> Aut(T2), where T2 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.
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