Abstract
For any right-angled Artin group $A_{\Gamma}$, Charney-Stambaugh-Vogtmann
showed that the subgroup $U^0(A_{\Gamma}) \leq \text{Out}(A_{\Gamma})$
generated by Whitehead automorphisms and inversions acts properly and
cocompactly on a contractible space $K_{\Gamma}$. In the present paper we show
that any finite subgroup of $U^0(A_{\Gamma})$ fixes a point of $K_{\Gamma}$.
This generalizes the fact that any finite subgroup of $\text{Out}(F_n)$ fixes a
point of Outer Space, and implies that there are only finitely many conjugacy
classes of finite subgroups in $U^0(A_{\Gamma})$.