{
  "abstract": "For an ordinary finite presentation $P=\\langle x_1,\\ldots,x_n\\mid R\\rangle$, put $G(P)=F_n/\\langle\\langle R\\rangle\\rangle$. We construct a primitive-recursive predicate $V$ with $G(P)''=1 \\Longleftrightarrow \\exists c\\in\\mathbb{N}: V(P,c)=1$. Thus finite presentations of metabelian groups are recursively enumerable, answering Kourovka Problem 17.124. An effective form of the Bieri-Strebel covering construction, using signed Laurent relations and rational separation, gives a family of finitely presented metabelian groups cofinal under epimorphisms. Products of conjugates of defining relators witness these epimorphisms. The construction and enumeration theorem are formalized in Lean 4.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.10281",
  "author_total": 1,
  "authors": [
    {
      "name": "Achyuth Jayadevan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/djpmz0r0v0j2f.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.10281",
  "fulltext_url": null,
  "id": "djpmz0r0v0j2f",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.10281",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "arxiv",
      "math.LO"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7212179260",
  "pdf_url": "https://arxiv.org/pdf/2609.10281",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/djpmz0r0v0j2f.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:15Z",
      "native_id": "2609.10281",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.10281"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.LO",
      "subfield": "logic-foundations"
    }
  ],
  "title": "Finite presentations of metabelian groups: effective enumeration via Laurent relations",
  "title_text": "Finite presentations of metabelian groups: effective enumeration via Laurent relations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/djpmz0r0v0j2f",
  "venue": "arXiv",
  "versions": []
}