{
  "abstract": "The Group Epimorphism Problem (GpEpi) asks, given two finite groups $G_1$ and $G_2$, whether there exists a surjective group homomorphism, or epimorphism, from $G_1$ to $G_2$. When the input groups are given by their multiplication (Cayley) tables, the problem admits a quasipolynomial-time algorithm in general, but little is known about its complexity for structured classes of finite groups. In this paper, we study the computational complexity of GpEpi for several well-studied classes of finite groups. Our main results are polynomial-time epimorphism tests for several classes of groups for which polynomial-time isomorphism testing was previously known: Groups with Abelian normal Hall subgroups with cyclic complement; Groups with (product of) elementary Abelian normal Hall subgroup with elementary Abelian complement; and Groups with some constraints on their Abelian chief factors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.07429",
  "author_total": 3,
  "authors": [
    {
      "name": "Joshua A. Grochow"
    },
    {
      "name": "Pranjal Srivastava"
    },
    {
      "name": "Dhara Thakkar"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dvy7fvf6g800y.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.07429",
  "fulltext_url": null,
  "id": "dvy7fvf6g800y",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.07429",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "cs.DS"
    ],
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7211988470",
  "pdf_url": "https://arxiv.org/pdf/2609.07429",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dvy7fvf6g800y.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:58Z",
      "native_id": "2609.07429",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.07429"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Algorithms for Finite Group Epimorphism Testing",
  "title_text": "Algorithms for Finite Group Epimorphism Testing",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:58Z",
  "url": "https://research.draconitic.com/paper/dvy7fvf6g800y",
  "venue": "arXiv",
  "versions": []
}