Right-angled Artin groups as finite-index subgroups of their outer automorphism groups

Abstract

We prove that every right-angled Artin group occurs as a finite-index subgroup of the outer automorphism group of another right-angled Artin group. We furthermore show that the latter group can be chosen in such a way that the quotient is isomorphic to $(\mathbb{Z}/2\mathbb{Z}{)}^N$ for some $N$. For these, we give explicit constructions using the group of pure symmetric outer automorphisms. Moreover, we need two conditions by Day-Wade and Wade-Brück about when this group is a right-angled Artin group and when it has finite index.

17 pages, 4 figures; v2: small changes, mainly update of the appendix

References in corpus (4)

• Relative automorphism groups of right-angled Artin groups
• Between buildings and free factor complexes: A Cohen-Macaulay complex for Out(RAAGs)
• Right-angled Artin groups as finite-index subgroups of their outer automorphism groups
• A note on virtual duality and automorphism groups of right-angled Artin groups

Cited by in corpus (1)

• Right-angled Artin groups as finite-index subgroups of their outer automorphism groups