# A structure of the group of automorphisms of an infinite binary tree

My friend asked me to ask his question here. Where he can find (a paper or a book) containing a complete description (with the proof) of a structure of the group of automorphisms of an infinite binary tree?

Thanks.

• One more thing: The (almost) full automorphism group $Aut_+(T)$ is an HNN extension of $Aut(T,r)$ (the group described in your answer), where $r$ is a fixed vertex of $T$ (a "root"). Here $Aut_+(T)$ is the subgroup of $Aut(T)$ of index 2 consisting of automorphisms acting without inversions. The edge subgroup here is also well-understood, it is isomorphic to the direct product $Aut(T,r)\times Aut(T,r)$. – Misha Feb 4 '14 at 8:52