Rigidity of actions of branch groups on rooted trees and automorphism groups.
by
Rostislav Ivanovich Grigorchuk
Texas A&M Univerity & Steklov Institute of Mathematics, Moscow
Coauthors: J.S. Wilson, S. Sidki

In the first part of the talk I will speak about the joint result with J.S.Wilson about rigidity of actions of some branch groups on rooted trees. The theorem states that essentially there is only one such action. One of the consequences of this result is the statement that the automorphism group coinsides with the normalizer in the full automorphism group of a tree. The statements of the last type where proven by S.Sidki and by Lavrenyuk-Nekrashevych by completely different arguments.

In the second part of the talk I will speak about a joint result with S.Sidki. Namely, the group of outer automorphisms of a well known 3-generated 2-group of intermediate growth is computed.

Date received: October 7, 2002