2025/11/17 by Ke Wang, Qiang Zhang, Wang, Ke +3
Mathematics · #Geometric and Algebraic Topology #Mathematical Dynamics and Fractals #Rings, Modules, and Algebras
paper · pdf · doi:10.48550/arxiv.2511.12871
In this paper, we first study the endomorphisms of free-abelian times surface groups and give a characterization of when they are injective and surjective. Then, we see that free-abelian times hyperbolic groups are Hopfian but not co-Hopfian. Moreover, we give a complete classification of fixed subgroups of endomorphisms in free-abelian times surface groups, which extends that of automorphisms. Finally, we study the endomorphisms of free-abelian times non-elementary torsion-free hyperbolic groups and give an equivalent condition for them to contain, up to isomorphism, finitely many end-fixed subgroups.