Outer automorphism groups of graph products: subgroups and quotients

We show that the outer automorphism groups of graph products finitely generated abelian satisfy Tits alternative, are residually finite, their so-called Torelli subgroups generated, and they a dichotomy between being virtually nilpotent containing non-abelian free subgroup is determined by graphical condition on underlying labelled graph. Graph simultaneously generalize right-angled Artin (RAAGs) Coxter (RACGs), providing common framework for studying these groups. Our results extend number known RAAGs and/or RACGs variety authors, including Caprace, Charney, Day, Ferov, Guirardel, Horbez, Minasyan, Vogtmann, Wade, current authors.