{
  "abstract": "We generalize a method devised by Mark and Paupert for finding group presentations of the single-cusped standard Picard modular groups $\\text{PU}(2, 1; \\mathcal{O}_d)$, where $\\mathcal{O}_d$ is the ring of integers of $\\mathbb{Q}(i\\sqrt{d})$, to a more general class of lattices in $\\text{PU}(2, 1)$. As an application, we give presentations for the so-called \\textit{sisters} of the standard Picard modular groups for $d=3, 7,$ and $11$. In particular, this shows that the sister of $\\text{PU}(2, 1; \\mathcal{O}_7)$ is a perfect group.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40568",
  "author_total": 1,
  "authors": [
    {
      "name": "Jackson Young"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d4fm76b84sf00.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40568",
  "fulltext_url": null,
  "id": "d4fm76b84sf00",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40568",
  "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.GT"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40568",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d4fm76b84sf00.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:35Z",
      "native_id": "2610.40568",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40568"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Presentations for sisters of one-cusped Picard modular groups",
  "title_text": "Presentations for sisters of one-cusped Picard modular groups",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:53Z",
  "url": "https://research.draconitic.com/paper/d4fm76b84sf00",
  "venue": "arXiv",
  "versions": []
}