arXiv:2501.05283 · v2

On the complexity of epimorphism testing with virtually abelian targets

首次提交 2025-01-09 22:45

版本更新 2026-10-28 11:35

雷达观测 2026-10-30 09:53

摘要

Friedl and Löh (2021, Confl. Math.) prove that testing whether or not there is an epimorphism from a finitely presented group to the direct product of an abelian and a finite group, or to a virtually cyclic group, is decidable. Here we prove that these problems are $\mathsf{NP}$-complete. In addition, we show that testing epimorphism is $\mathsf{NP}$-complete when the target is is the semi-direct product of a finitely generated free-abelian group and a finite group which factors through $\{\pm\text{Id}\}$, thus extending the class of virtually abelian target groups for which decidability of epimorphism is known.

作者备注：27 pages. Sections 7-9 of previous version of this paper split into a separate article arxiv:TBA