Artin HNN-extensions virtually embed in Artin groups

TL;DR

The paper proves that certain Artin HNN-extensions can be embedded into Artin groups, and similarly for Coxeter groups, revealing new structural relationships among these groups.

Contribution

It demonstrates that some finite index subgroups of Artin HNN-extensions embed into Artin groups, extending understanding of their algebraic structure.

Findings

Finite index subgroups of Artin HNN-extensions embed in Artin groups

Analogous embedding results hold for Coxeter groups

Provides new insights into the subgroup structure of Artin and Coxeter groups

Abstract

An Artin HNN-extension is an HNN-extension of an Artin group in which the stable letter conjugates a pair of suitably chosen subsets of the standard generating set. We show that some finite index subgroup of an Artin HNN-extension embeds in an Artin group. We also obtain an analogous result for Coxeter groups.