On consecutive factors of the lower central series of right-angled Coxeter groups (Q6636265)

The authors study right-angled Coxeter groups and their lower central series. In particular, a right-angled Coxeter group is by definition a finitely presented group whose generators are involutions and satisfy commutation relations given by an undirected graph. These infinite groups arise naturally as the topological fundamental groups of polyhedral products of \(\mathbb RP^{\infty}\).\N\NThe lower central series of any abstract group is a family of abelian groups, each of which comes with a natural Lie bracket. The authors give some new insights into the structure of the derived series of right-angled Coxeter groups. The tool for this is their \textit{Magnus mapping}, which embeds any right-angled Coxeter group into the tensor algebra of an \(\mathbb F_2\)-vector space. For any right-angled Coxeter group associated with a graph with four vertices, they use this to explicitly describe the fourth group in the lower central series.