{
  "abstract": "Let $M$ be a module over a commutative ring with unity $R$, and let $ϕ:M \\to R$ be an $R$-linear map. Then the product $mn = m + (1+ϕ(m))n$ defines a monoid $Mon(ϕ)$ on $M$. We show that if $G$ is a group, then $G$ arises as the group of invertible elements of some such monoid $Mon(ϕ)$ if and only if $G$ is metabelian.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.35603",
  "author_total": 1,
  "authors": [
    {
      "name": "Lorenzo Traldi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3ty2rsb9sqvpc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.35603",
  "fulltext_url": null,
  "id": "3ty2rsb9sqvpc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.35603",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.GR"
    ],
    [
      "openalex",
      "2607|Finite Group Theory Research"
    ]
  ],
  "openalex": "W7223908042",
  "pdf_url": "https://arxiv.org/pdf/2610.35603",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3ty2rsb9sqvpc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.35603",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.35603"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Modular representations of metabelian groups",
  "title_text": "Modular representations of metabelian groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/3ty2rsb9sqvpc",
  "venue": "arXiv",
  "versions": []
}