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On verbal subgroups of the group of automorphisms of regular rooted trees

Costantino Delizia, Mikel E. Garciarena, Marialaura Noce

Abstract

In this paper we revisit the description of all verbal subgroups of the group of automorphisms of a regular rooted tree $\mathcal{T}_d$, for $d>2$ and odd.

On verbal subgroups of the group of automorphisms of regular rooted trees

Abstract

In this paper we revisit the description of all verbal subgroups of the group of automorphisms of a regular rooted tree , for and odd.
Paper Structure (4 sections, 19 theorems, 73 equations)

This paper contains 4 sections, 19 theorems, 73 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. First results
  4. Verbal subgroups

Key Result

Lemma 1

Every element of $\mathop{\mathrm{Aut}}\nolimits{\mathcal{T}}$ is conjugate to its inverse.

Theorems & Definitions (37)

  • Lemma 1: Conjugate_of_its_inverse
  • Lemma 2: Cyclic_renormalization
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Theorem 5
  • proof
  • Corollary 6
  • proof
  • ...and 27 more