Reflection subgroups of odd-angled Coxeter groups

TL;DR

This paper provides a criterion based on prime divisors of Coxeter relation exponents to determine when an odd-angled Coxeter group has a finite index reflection subgroup.

Contribution

It introduces a new criterion linking prime divisors of exponents to the existence of proper finite index reflection subgroups in odd-angled Coxeter groups.

Findings

Criterion based on least prime divisors of exponents

Applicable to finitely generated odd-angled Coxeter groups

Characterizes when such groups have proper finite index reflection subgroups

Abstract

We give a criterion for a finitely generated odd-angled Coxeter group to have a proper finite index subgroup generated by reflections. The answer is given in terms of the least prime divisors of the exponents of the Coxeter relations.