On the automorphism group of the one-rooted binary tree

[摘要] Let A be the automorphism group of the one-rooted regular binary tree T-2 and G the subgroup of A consisting of those automorphisms admitting a ''finite description'' in their action on T-2. Let N-A(G) be the normaliser of G in A, let Aut(G) be the group of automorphisms of G, and let End(A)(G) be the semigroup of endomorphisms of G induced by conjugation by elements of A. Then G is the infinite iterated wreath product (... (sic) C-2) (sic) C-2, and A is the topological limit of G. We study in some detail the structure of G, Aut(G), and End(A)(G). In particular, we prove N-A(G) is isomorphic to Aut(G), contains a copy of A itself, and is a proper subgroup of End(A)(G). Furthermore we discuss connections with automata and introduce the notion of functionally recursive automorphisms of T-2. (C) 1997 Academic Press.

[发布日期] 1997-09-15