Faithful Group Actions on Rooted Trees Induced by Actions of Quotients
Yaroslav Lavrenyuk, Volodymyr Mazorchuk, Andriy Oliynyk, Vitaliy Sushchansky · Communications in Algebra · 2007
We develop some new techniques of constructing (finite state) actions on rooted homogeneous trees and apply them to various groups. In particular we show that there is a faithful action of each amalgameted free product of the form ℤ∗ℤℤ on a rooted homogeneous tree of finite degree, described by finite state automorphisms.