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The classical result by Dyer--Scott about fixed subgroups of finite orderautomorphisms of $F_n$ being free factors of $F_n$ is no longer true in$Z^m\times F_n$. Within this more general context, we prove a relaxed versionin the spirit of Bestvina--Handel Theorem: the rank of fixed subgroups offinite order automorphisms is uniformly bounded in terms of $m,n$. We alsostudy periodic points of endomorphisms of $Z^m\times F_n$, and give analgorithm to compute auto-fixed closures of finitely generated subgroups of$Z^m\times F_n$. On the way, we prove the analog of Day's Theorem for realelements in $Z^m\times F_n$, contributing a modest step into the project ofdoing so for any right angled Artin group (as McCool did with respect toWhitehead's Theorem in the free context).

Fixed subgroups and computation of auto-fixed closures in free-abelian times free groups