On the Derived Series of 3- and 4-Generator Coxeter Groups

Abstract

Let G be a group and let φ (G) be the least integer k such that G(k)=G(k+1). If no such k exists, then φ (G)=∞ and we write G ∈ 𝓤. We are interested in the questions which Coxeter groups are in 𝓤 and how large a finite number φ (G) can be for Coxeter groups G. In this paper, we give full answers in the 3- and 4-generator cases.