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. 



A structure of the group of automorphisms of an infinite binary tree
I am assuming you mean a binary rooted tree. I don't know your definition of complete. The group is the infinite permutational wreath product of symmetric groups of degree 2. Good references are [Automata, dynamical systems and infinite groups](http://www.math.tamu.edu/~grigorch/publications/PSIM128.PS) by R. Grigorchuk, V.V.Nekrashevich, V.I.Sushchanskii, Proc. Steklov Inst. Math. v.231 (2000), 134-214 and Cyclic renormalization and automorphism groups of rooted trees by Bass, Otero-Espinar, and Rockmore.


