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On the Automorphism Group of the One-Rooted Binary Tree

✍ Scribed by A.M. Brunner; Said Sidki

Publisher
Elsevier Science
Year
1997
Tongue
English
Weight
339 KB
Volume
195
Category
Article
ISSN
0021-8693

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✦ Synopsis

Let A be the automorphism group of the one-rooted regular binary tree T and 2 G the subgroup of A consisting of those automorphisms admitting a ''finite Ε½ . description'' in their action on T . Let N G be the normaliser of G in A, let 2 A Ε½ . Ε½ . Aut G be the group of automorphisms of G, and let End G be the semigroup of A endomorphisms of G induced by conjugation by elements of A. Then G is the Ε½ . infinite iterated wreath product . . . X C X C , and A is the topological limit of 2 2

Ε½ . Ε½ . G. We study in some detail the structure of G, Aut G , and End G . In A Ε½ .

Ε½ . particular, we prove N G is isomorphic to Aut G , contains a copy of A itself, A Ε½ . and is a proper subgroup of End G . Furthermore we discuss connections with A automata and introduce the notion of functionally recursive automorphisms of T .

2

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