Josimar da Silva Rocha. The n-ary Adding Machine and Soluble Groups
Natural Sciences / Mathematics / Algebra
Submitted on: Mar 27, 2012, 17:44:18
Description: We describe under a variety of conditions abelian subgroups of the automorphism group A of the regular n-ary tree T 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 a prime number, and for n = 4 we prove that every finitely generated soluble subgroup of A containing t is an extension of a torsion-free metabelian group by a finite group.