Right-angled Artin subgroups and free products in one-relator groups

Abstract

We investigate criteria ensuring that a one-relator group $G$ contains a right-angled Artin subgroup $A(\Gamma )$, corresponding to a finite graph $\Gamma$. In particular, we prove that if $\Gamma$ is a forest with at least one edge and the positive submonoid $T(\Gamma )$, of $A(\Gamma )$, embeds into $G$ then so does all of $A(\Gamma )$. As by-products of our methods we obtain characterisations of one-relator groups that have property $P_{nai}$ and that are $C^{\ast }$-simple.

arXiv comment35 pages, 4 figures; this version is accepted for publication in Annales de l'Institut Fourier