Narrow normal subgroups of Coxeter groups and of automorphism groups of Coxeter groups

TL;DR

This paper characterizes the structure of finite and narrow normal subgroups within Coxeter groups and their automorphism groups, providing insights into their subgroup composition.

Contribution

It introduces a detailed description of finite and narrow normal subgroups in Coxeter and automorphism groups, a novel structural analysis.

Findings

Finite and narrow normal subgroups are explicitly characterized.

Automorphism groups of Coxeter groups contain specific types of normal subgroups.

The structure of narrow subgroups excludes non-abelian free groups.

Abstract

By definition, a group is called narrow if it does not contain a copy of a non-abelian free group. We describe the structure of finite and narrow normal subgroups in Coxeter groups and their automorphism groups.