Rotation groups virtually embed into right-angled rotation groups

TL;DR

This paper generalizes a known embedding theorem for reflection groups to a broader class called rotation groups, showing they virtually embed into right-angled rotation groups, thus extending the understanding of their algebraic structure.

Contribution

It proves that rotation groups, a generalization of Coxeter groups and graph products, virtually embed into right-angled rotation groups, broadening the scope of embedding theorems.

Findings

Rotation groups virtually embed into right-angled rotation groups.

Generalization of the embedding theorem from reflection groups to rotation groups.

Extension of algebraic embedding results to a wider class of groups.

Abstract

It is a theorem due to F. Haglund and D. Wise that reflection groups (aka Coxeter groups) virtually embed into right-angled reflection groups (aka right-angled Coxeter groups). In this article, we generalise this observation to rotation groups, which can be thought of as a common generalisation of Coxeter groups and graph products of groups. More precisely, we prove that rotation groups (aka periagroups) virtually embed into right-angled rotation groups (aka graph products of groups).