Classification of Fixed Subgroups of Endomorphisms in Free-abelian Times Surface Groups
Group Theory
2025-11-18 v1 Geometric Topology
Abstract
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.
Cite
@article{arxiv.2511.12871,
title = {Classification of Fixed Subgroups of Endomorphisms in Free-abelian Times Surface Groups},
author = {Ke Wang and Qiang Zhang and Dongxiao Zhao},
journal= {arXiv preprint arXiv:2511.12871},
year = {2025}
}
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16 pages