Wreath operations in the group of automorphisms of the binary tree

Journal of Algebra

Volumn 257, Issue 1, 2002, Pages 51-64

  Brunner, A M ^a   Sidki, Said ^b  

^a UNIVERSITY OF WISCONSIN PARKSIDE   (United States)

^b UNIVERSITY OF BRASILIA   (Brazil)

Author keywords

Automata; Binary tree; Pro p group; Wreath product

Indexed keywords

EID: 0036874604     PISSN: 00218693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-8693(02)00050-9     Document Type: Article

References (12)

1. L. Bartholdi, R. Grigorchuk, Z. Šunik, Branch groups, to appear.
2. A.M. Brunner, S. Sidki, On the automorphism group of the one-rooted binary tree, J. Algebra 195 (1997)465-486.
3. A.M. Brunner, S. Sidki, The generation of GL(n, ℤ) by finite-state automata, Internat. J. Algebra Comput. 8 (1998) 127-139.
4. A.M. Brunner, S. Sidki, A.C. Vieira, A just-nonsolvable torsion-free group defined on the binary tree, J. Algebra 211 (1999) 99-114.
5. V.V. Nekrashevych, S. Sidki, Automorphisms of the binary tree: state-closed subgroups and dynamics of 1/2-endomorphisms, in: Proc. Conf. on Group Theory, Bielefeld, 1999.
6. K.W. Gruenberg, Residual properties of infinite soluble groups, Proc. London Math. Soc. (3) 7 (1957) 29-62.
7. R.I. Grigorchuk, Growth rates of finitely generated groups and theory of invariant means, Izv. Akad. Nauk SSSR, Set. Mat. 48 (1984) 939-985.
8. R.I. Grigorchuk, V.V. Nekrashevych, V.I. Sushchanskii, Automata, dynamical systems, and groups, Proc. Steklov Inst. 231 (2000) 128-203.
9. P. Hall, Finiteness conditions for soluble groups, Proc. London Math. Soc. (3) 4 (1954) 413-496.
10. M.I. Kargapolov, Ju.I. Merzljakov, Fundamental Theory of Groups, in: Graduate Texts in Math., Vol. 162, Springer-Verlag, 1979.
11. V.N. Remeslennikov, V.G. Sokolov, Certain properties of the Magnus embeddings, Algebra i Logika 9 (1970) 566-578.
12. S. Sidki, Automorphisms of one-rooted trees: growth, circuit structure and acyclicity, J. Math. Sci. 100 (2000) 1925-1943.