{
  "abstract": "In this work, we study the self-similarity of permutational wreath products of the form \\(A \\wr_X G\\), where \\(A\\) is a finitely generated abelian group and \\(G\\) is a self-similar group (the permutational wreath product \\(A \\wr_X G\\) is also known as a lamplighter group). In the case where \\(G\\) is a non-torsion contracting group, we prove that, under certain conditions, the Scott--Röver--Nekrashevych group \\(V_m(\\mathbb{Z}^d \\wr_X G)\\) is finitely presented and virtually simple. Moreover, we prove that \\(\\mathbb{Z}^d \\wr_X G\\) embeds into a finitely presented simple group. Furthermore, this provides a new family of groups that satisfy the Boone--Higman conjecture.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.01868",
  "author_total": 3,
  "authors": [
    {
      "name": "Mailton Rego Almeida"
    },
    {
      "name": "Alex Carrazedo Dantas"
    },
    {
      "name": "Altair Santos de Oliveira-Tosti"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5q5e6g52dcvpb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.01868",
  "fulltext_url": null,
  "id": "5q5e6g52dcvpb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.01868",
  "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",
      "math.GR"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7207629898",
  "pdf_url": "https://arxiv.org/pdf/2609.01868",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-15",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5q5e6g52dcvpb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:30:37Z",
      "native_id": "2609.01868",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.01868"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GR",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "On the Self-Similarity of Permutational Wreath Products and Their Embedding into Finitely Presented Simple Groups",
  "title_text": "On the Self-Similarity of Permutational Wreath Products and Their Embedding into Finitely Presented Simple Groups",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:31Z",
  "url": "https://research.draconitic.com/paper/5q5e6g52dcvpb",
  "venue": "arXiv",
  "versions": []
}