2024/01/15 by André Carvalho, Carvalho, André, Jordi Delgado +1
Computer Science · Mathematics · #20E06 #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2401.07821
openalex publication_date 2024/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We obtain an explicit description of the endomorphisms of free-abelian by free groups together with a characterization of when they are injective and surjective. As a consequence we see that free-abelian by free groups are Hopfian and not coHopfian, and we investigate the isomorphism problem and the Brinkmann Problem for this family of groups. In particular, we prove that the isomorphism problem (undecidable in general) is decidable when restricted to finite actions, and that the Brinkmann Problem is decidable both for monomorphisms and automorphisms.