MUTUAL EMBEDDINGS OF RIGHT-ANGLED ARTIN GROUPS AND GENERALIZED BAUMSLAG-SOLITAR GROUPS

Abstract

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.