Josimar da Silva Rocha and Said Najati Sidki. The n-ary adding machine and soluble groups.
Submitted on: May 30, 2012, 12:00:52
Natural Sciences / Mathematics / Algebra
Description: We describe under a various conditions abelian subgroups of the automorphism group Aut(Tn) of the regular n-ary tree Tn, which are normalized by the n-ary adding machine τ=(e...,e,τ)σ, where τ isthe n-cycle (0, 1, ..., n-1). As an application, for n = p a prime number, and for n = p^2 when p = 2, we prove that every finitely generated soluble subgroup of Aut(Tn), containing τ is an extension of a torsion-free metabelian group by a finite group.
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