Hyperreflection groups

TL;DR

This paper introduces hyperreflection groups as a broad generalization of Coxeter groups, establishing foundational properties and showing that Coxeter groups and graph products are special cases.

Contribution

The paper defines hyperreflection groups, proves key properties like Deletion and Exchange Conditions, and demonstrates that Coxeter groups and graph products are examples.

Findings

Hyperreflection groups generalize Coxeter groups.

Proved Deletion and Exchange Conditions for hyperreflection groups.

Coxeter groups and graph products are special cases.

Abstract

We introduce the concept of hyperreflection groups, which are a generalization of Coxeter groups. We prove the Deletion and Exchange Conditions for hyperreflection groups, and we discuss special subgroups and fundamental sectors of hyperreflection groups. In the second half of the paper, we prove that Coxeter groups and graph products of groups are examples of hyperreflection groups.