English

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.

Keywords

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

R2 v1 2026-06-21T18:51:22.680Z