ON FINITE GENERATION OF SELF-SIMILAR GROUPS OF FINITE TYPE
Ievgen Bondarenko, Igor O. Samoilovych · International Journal of Algebra and Computation · 2012
A self-similar group of finite type is the profinite group of all automorphisms of a regular rooted tree that locally around every vertex act as elements of a given finite group of allowed actions. We provide criteria for determining when a self-similar group of finite type is finite, level-transitive, or topologically finitely generated. Using these criteria and GAP computations we show that for the binary alphabet there is no infinite topologically finitely generated self-similar group given by patterns of depth 3, and there are 32 such groups for depth 4.