The Group of Balanced Automorphisms of a Spherically Homogeneous Rooted Tree

• Autorzy: Adam Woryna
• Języki publikacji: EN

Abstrakty

EN

Let X* be a tree of words over the changing alphabet (Xo, X1,. . .) with Xi = {0,1,...,mi - 1}, mi > 1. We consider the group Aut(X*) of automorphisms of a tree X* . A cyclic automorphism of X* is called constant if its root permutations at any two words from the same level of X* coincide. In this paper we introduce the notion of a balanced automorphism which is obtained from a constant automorphism by changing root permutations at all words ending with an odd letter for their inverses. We show that the set of all balanced automorphisms forms a subgroup of Aut(X *) if and only if 2 \ mi implies mi+1 = 2 for i = 0, 1, . . . . We study, depending on a branch index of a tree, the algebraic properties of this subgroup.(original abstract)

Słowa kluczowe

EN

Mathematics; Mathematical analysis

PL

Matematyka; Analiza matematyczna

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2009
• Tom: 23
• Strony: 83--101

Twórcy

autor

Adam Woryna

• Silesian University of Technolog, Gliwice, Poland

Bibliografia

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• Nekrashevych V., Self-similar Groups, Math. Surveys Monogr., Vol.117, Amer. Math. Soc., Providence, RI., 2005.
• Sidki S., Regular Trees and their Automorphisms, Monografias de Matematica, Vol. 56, IMPA, Rio de Janeiro, 1998.