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A note on right-angled Artin subgroups of one-relator groups

Carl-Fredrik Nyberg-Brodda

Abstract

We give a short proof of the following result due to Howie: if $A(Γ)$ is a right-angled Artin group embedding into some one-relator group, then $Γ$ is a finite forest. The proof only uses elementary Bass--Serre theory and classical properties of one-relator groups.

A note on right-angled Artin subgroups of one-relator groups

Abstract

We give a short proof of the following result due to Howie: if is a right-angled Artin group embedding into some one-relator group, then is a finite forest. The proof only uses elementary Bass--Serre theory and classical properties of one-relator groups.

Paper Structure

This paper contains 2 sections, 1 theorem, 1 equation.

Table of Contents

  1. 1.
  2. 2.

Key Result

Lemma 1.1

Let $G$ be a group acting on a tree $\mathcal{X}$ without inversion. If $g, h \in G$ are commuting elliptic elements, then $\mathop{\mathrm{Fix}}\nolimits(g) \cap \mathop{\mathrm{Fix}}\nolimits(h) \neq \varnothing$. If $g \in G$ is a loxodromic element and $h \in C_G(g)$, then the following both hol

Theorems & Definitions (1)

  • Lemma 1.1