Finite groups of untwisted outer automorphisms of RAAGs

For any right-angled Artin group A , Charney, Stambaugh and Vogtmann showed that the subgroup U 0 .A / Out.A / generated by Whitehead automorphisms and inversions acts properly and cocompactly on a contractible space K .We show that any finite subgroup of U 0 .A / fixes a point of K .This generalizes the fact that any finite subgroup of Out.F n / fixes a point of outer space, and implies that there are only finitely many conjugacy classes of finite subgroups in U 0 .A /. 20F28, 20F36, 20F65