Incoherent Coxeter Groups

TL;DR

This paper demonstrates that many Coxeter groups, especially those with uniform exponent greater than 2 and numerous generators, are incoherent using probabilistic methods.

Contribution

It introduces probabilistic techniques to prove incoherence in broad classes of Coxeter groups, expanding understanding of their algebraic properties.

Findings

Coxeter groups with uniform exponent > 2 are incoherent

Probabilistic methods effectively prove incoherence

Incoherence holds for groups with sufficiently many generators

Abstract

We use probabilistic methods to prove that many Coxeter groups are incoherent. In particular, this holds for Coxeter groups of uniform exponent > 2 with sufficiently many generators.