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PreprintCC BY 4.0arXiv

Epimorphism testing with dihedral targets

  • Murray Elder
  • Jerry Shen
  • Armin Weiß
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Abstract

We consider the problem of deciding whether or not there is an epimorphism from the class of finitely presented groups to a fixed finite group. We show this problem is NP-complete when the target is a non-nilpotent dihedral group. This complements work of Kuperberg and Samperton (2018, Geom. Topol.) who showed the same result when the target is a fixed finite non-abelian simple group. We also include a survey of complexity and reduction results when the source and target are classes of finitely presented groups.

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Cite

BibTeXRIS
BibTeX
@misc{elder2026epimorphism,
  title = {{Epimorphism testing with dihedral targets}},
  author = {Murray Elder and Jerry Shen and Armin Weiß},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.39487},
  eprint = {2610.39487},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.39487},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Epimorphism testing with dihedral targets
AU  - Murray Elder
AU  - Jerry Shen
AU  - Armin Weiß
PY  - 2026
DA  - 2026/10/29
PB  - arXiv
DO  - 10.48550/arxiv.2610.39487
UR  - https://arxiv.org/abs/2610.39487
AB  - We consider the problem of deciding whether or not there is an epimorphism from the class of finitely presented groups to a fixed finite group. We show this problem is NP-complete when the target is a non-nilpotent dihedral group. This complements work of Kuperberg and Samperton (2018, Geom. Topol.) who showed the same result when the target is a fixed finite non-abelian simple group. We also include a survey of complexity and reduction results when the source and target are classes of finitely presented groups.
ER  -