On the finiteness properties of fixed subgroups of automorphisms

We use Sigma-invariants to study homotopical and homological finiteness properties of fixed subgroups of automorphisms of a group $G$ in terms of its center $Z(G)$ and the induced automorphisms on its associated quotient $G/Z(G)$. Specializing to the case where the center is a direct factor of the group, we answer a question made by Lei, Ma and Zhang.