The n-ary Adding Machine and Soluble Groups
Group Theory
2013-07-10 v4
Abstract
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 soluble subgroup of A containing t is an extension of a torsion-free metabelian group by a finite group.
Cite
@article{arxiv.1108.3373,
title = {The n-ary Adding Machine and Soluble Groups},
author = {Josimar da Silva Rocha and Said Najati Sidki},
journal= {arXiv preprint arXiv:1108.3373},
year = {2013}
}
Comments
46 pages