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.
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. 


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 by R. Grigorchuk, V.V.Nekrashevich, V.I.Sushchanskii, Proc. Steklov Inst. Math. v.231 (2000), 134214 and Cyclic renormalization and automorphism groups of rooted trees by Bass, OteroEspinar, and Rockmore. 


Topics in geometric group Theory by P. de la Harpe should also contain this and is very well written. 

