AUTOMORPHISM AND OUTER AUTOMORPHISM GROUPS OF RIGHT-ANGLED ARTIN GROUPS ARE NOT RELATIVELY HYPERBOLIC

Abstract We show that the automorphism groups of right-angled Artin whose defining graphs have at least three vertices are not relatively hyperbolic. then outer also hyperbolic, except for a few exceptional cases. In these cases, virtually isomorphic to either finite group, an infinite cyclic group or $\mathrm {GL}_2(\mathbb {Z})$ .