Polyhedral products, and relations in the commutator subgroup of a right-angled Coxeter group

Abstract

We give a criterion of the existence of a presentation with a single relation for the commutator subgroup $R{C}_{\mathcal{K}}^{\prime }$ of a right-angled Coxeter group $R{C}_{\mathcal{K}}$. Namely, we prove that $R{C}_{\mathcal{K}}^{\prime }$ is a one-relator group if and only if $\mathcal{K}$ is either a $p$-cycle with $p⩾4$ or has the form ($p$-cycle)$\ast {\Delta }^q$ with $p⩾4$ and $g⩾0$, where ${\Delta }^q$ is a $q$-simplex.

This paper has been subsumed into arXiv:2002.11476

References in corpus (2)

• Pontryagin algebras of some moment-angle-complexes
• Families of minimally non-Golod complexes and their polyhedral products