Embedding Right-Angled Artin Groups into Brin-Thompson Groups

Abstract

We prove that every finitely-generated right-angled Artin group can be embedded into some Brin-Thompson group $nV$. It follows that many other groups can be embedded into some $nV$ (e.g., any finite extension of any of Haglund and Wise's special groups), and that various decision problems involving subgroups of $nV$ are unsolvable.