Mutual embeddings of right-angled Artin groups and generalized Baumslag-Solitar groups

Abstract

A finitely generated group G acting on a tree so that all
vertex and edge stabilizers are infinite cyclic groups is called a generalized
Baumslag–Solitar group (GBS group). In this paper, we study when
a given GBS group can be embedded in a right-angled Artin group
(RAAG) and vice versa. An exhaustive description has been obtained
in both cases. If an embedding exists, then we discuss its construction.