Josimar da Silva Rocha and Said Najati Sidki. The n-ary adding machine and soluble groups
Natural Sciences / Mathematics / Algebra
Submitted on: Sep 02, 2012, 11:31:39
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 t=(e...,e,t)s, where s is the 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 t is an extension of a torsion-free metabelian group by a finite group.
The full-text article has been published in the "IntellectualArchive" journal , Vol.1, Num.4, August 2012, ISSN 1929-4700.