Embedding Right-Angled Artin Groups into Brin-Thompson Groups

TL;DR

This paper demonstrates that all finitely-generated right-angled Artin groups can be embedded into Brin-Thompson groups, revealing new connections and undecidability results in group theory.

Contribution

It proves the embedding of finitely-generated right-angled Artin groups into Brin-Thompson groups, expanding understanding of subgroup structures and decision problems.

Findings

All finitely-generated right-angled Artin groups embed into some $nV$

Many other groups, including certain extensions, also embed into $nV$

Some subgroup decision problems in $nV$ are undecidable

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.