Fixed Subgroups of Endomorphisms of Free Products

Abstract

Let $G={\ast }_{i=1}^n{G}_i$ and let $\varphi$ be a symmetric endomorphism of $G$. If $\varphi$ is a monomorphism or if $G$ is a finitely generated residually finite group, then the fixed subgroup $Fix(\varphi )=\{g\in G:\varphi (g)=g\}$ of $\varphi$ has Kurosh rank at most $n$.

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